Personally, I wouldn't worry much, at least not for april of next year.
In 2024, easter is in march. So the easter crowds will already have started before, and the next wave should start walking a bit later, more towards end of april/may. Therefore you should be between waves, which makes it easier to just wing it without too many problems.
In a year when easter is in april it might be more complicated, but still doable, in my opinion (I walked during easter on my first Camino, and it was busy, but I still always got a bed just showing up).
But it also depends on what you expect from your accommodation and how willing/able you're to adapt.
If you want to get a single room with own bathroom at the first place you try, arriving at 8pm, then a reservation would be the better approach. If you want to ship luggage you'll also need to make reservations.
But if you're okay with dormitorios, carry your backpack and (in a worst case scenario, which in my experience is rare) you'd be fine with a mattress on the floor, or a spot in an overflow to put down your own sleeping mat, and with maybe walking a few kms further to the next albergue or town, most likely you'll be fine, I think (no guarantees of course).
The more fancy albergues that can be booked via booking.com can fill up quickly, especially during busy months - but that doesn't necessarily mean there are no beds. Often when the fancy places are all fully booked for days, you still get a bed in the more basic albergue next door as a walk-in.
If that sounds okay to you, parroquial and municipal albergues is what to look for.
Another strategy would be to walk off-stage and stay in smaller villages before/after the popular stopping points, or on variants (Valcarlos vs. Orisson, for example).
If all fails, you can still switch to reservations if needed (same or next day is usually enough).
Anyway, Happy planning and Buen Camino!
