First off, I absolutely love that you're reaching out for feedback like this and I hope I'm not too late to the party, because I'd like to pitch in my two eurocents.
There's a lot of valuable feedback posted already on very specific topics, so I'll try to approach the subject from a more holistic angle, looking at the different phases of the game and how they are treated in some of the successful games of the genre (no, I'm not saying PoE should copy Fortnite).
Early game:
In PoE Royale, you spawn in a random spot on the beach. When the countdown ends, you frantically rush inwards, hoping to snag a box of supplies or a stash before the exiles who spawned close to you get there. If you manage to snag a good skill gem, you continue your mad dash towards the ramps inwards to hopefully get or maintain an experience lead. If a good rare or some movement speed boots drop for you, nice, but you can't really afford to spend time farming for these at this stage. If someone else snags the good gems ahead of you, you're relegated to scavenging for stashes other players might have missed since you can't reliably force an engagement with whoever stole your loot, if they don't want to stand and fight.
In other notable Battle Royale (BR) games, you have some choice regarding your starting location. Do you drop towards one of the more desirable areas knowing that you'll most likely have to fight off other players early game or do you go for something more remote, settling for less early game loot in return for a safer and less hectic start to the game? As you drop in, you'll get a feeling for how many other players chose a location close to yours, and their relative position to yourself, preparing you for the likely encounters. Disengaging from other players can be a difficult and risky process since gunfire is likely to end the game for anyone who just turns and runs.
In other BRs, more than half of the players generally proceed from the early game in some form of fighting condition. If you are eliminated, it is generally in a fair fight with other players or due to an ambush. In PoE Royale, it currently feels like as much as 80% of the players are effectively eliminated on the beach, falling too far behind on the exp train to ever become relevant threats. The main actual elimination comes from someone picking a bad fight out of desperation, hoping for that 10% chance to snag a good skill and some needed exp.
Observation: The amount of "effective eliminations" is a problem. Eliminations should be due to pvp rather than falling irrecoverably behind or feeling like that is the case.
Observation: We want players to feel like they have agency and meaningful decisions to make in the early game. There seems to be a consensus building that the best strategy is restarting until you happen upon an inherently strong start.
Midgame:
Experience is the name of the PoE Royale mid game. You're probably picking up some potentially relevant loot too and starting to allocate some passive points, but better not spend too much time on anything except moving inwards and killing mobs. This stage is pretty similar to racing since the most successful players are those who can juggle their inventory and skills while blasting through the mobs. If you fall behind here or if you fell behind in the early game, the map will start to feel empty as the other players clear ahead of you, and you will probably find skills and gear with level requirements that make them unusable for you. "Fair" fights are rare and kills generally occur when one player is distracted by looting or otherwise managing their character, and/or if the other player is significantly stronger while having a movement skill advantage to quickly chase down their victim.
In other BRs, the pace generally calms down during the midgame. With the early fights around the drop zones finished, players or teams have to balance chasing additional loot and equipment with trying to get into a good tactical position for the late game conflicts. Some will look to recover from a weak start or catapult themselves further ahead by attempting to get the drop on other players and eliminate the opposition while getting more loot, but most skirmishes occur as players naturally gravitate towards the points of interest on the map.
Observation: PoE has a complex and deep system for character customization, but you get punished harshly if you spend too much time engaging with it. You need to know your plan for the different skills ahead of time, and be able to recognize potentially relevant items at a glance. This makes the mode very unforgiving for new players.
Observation: While "kills of opportunity" happen, players are generally better off playing PvE than pursuing conflict in this phase. Note that this isn't necessarily an issue.
Observation: The island starts to feel small and barren during this stage, if you're not leading the pack. You can end up spending a lot of time combing through the area for mobs missed by the players before you with no clear goal or destination.
Late Game:
You've reached the center of the map, and most of the monsters have been cleared out. Now is the time to fiddle with your inventory and optimize your gear. If you lack crucial pieces you can go scavenging, otherwise try to get the drop on an inattentive victim. As the arena border starts to close in, you might start to get a feeling for who your main opponents might be and try to tweak your gear and build accordingly. In the current state of PoE Royale that most likely means picking up the reduced phys/chaos dot node if you have extra passives and prioritizing fire resistance.
Whereas the pace slows down a bit in the PoE Royale late game, this is where it picks back up again and the game becomes more tense in other BRs. The contracting border forces campers to move out of their locations and forces more skirmishes in general. These are often highly lethal and chaotic as more than two or three parties might be involved at once.
Observation: The reduction in pace seems more accidental than deliberate as players run out of "stuff to do". The best players will have done most of the work on their builds during the mid game farming, and fights are generally avoidable unless there is a huge mobility advantage on one side.
Endgame:
While the endgame is the climax of the match, it is probably the least interesting part from a game design perspective. Players can no longer realistically avoid each other as the match devolves into a single perpetual fight for survival until eventually a single player stands victorious. I think PoE Royale has the potential to be more interesting than most other BRs here, as players may be forced to adopt their strategy and playstyles dramatically to combat the opposing builds.
Suggestions:
Increase the island size and/or reduce the amount of players. This should reduce the amount of players who are effectively eliminated during the initial rush for a skill gem.
If the above is not enough to prevent slower or unlucky players from being "locked out" from experience, you need to consider other ways of keeping them in the fight. An experience reward to all surviving players after each size reduction was mentioned by another poster and is an effective but somewhat inelegant approach.
Add more "points of interest" to the map in addition to the potion shrines and consider making them visible from an even greater distance than those. The potion shrines are a good start, but the reward is situational and players don't have to commit to a fight to get it - like with loot, you can probably jump in, click the shrine and disengage. Consider a similar shrine that spawned monsters - the experience and loot is always relevant, and players would have to stick around to reap the rewards. You could also consider requiring players to stay inside an area to activate the buff rather than doing it immediately on click. There's a lot of potential here for motivating players to seek out these points and force them to fight for the rewards.
If we look beyond PoE Royale today and which direction you could take it, I would personally prefer a less hectic game mode which allows you more breathing space to deliberate how to maximize your available skills, supports and items, trying to stitch together a unique build every match based on what you find. I do realize that this is very subjective though and might turn off many other players.
Thank you for reading, and thank you for making a great mode for a great game.