Cyanoacrylate, aka CA glue or superglue, is the best adhesive for PLA. After applying the glue, fixture or clamp together the parts you are planning to adhere and then leave them alone while the glue cures.

CA glue (aka super glue) works extremely well with PLA. I wouldn't recommend any special 3d print specific glue because it will probably be the same thing but with a higher price.

Super glue is fine. You don't need to waste money on expensive glues.

It's so good that recovering magnets from prints I've made takes a lot of work because the super glue holds them to pla really well.

Regular superglue for placing magnets, I like 3DGloop for sticking prints together

PLA to PLA: Gloop https://www.3dgloop.com/shop/pla-gloop

Sci-Grip 16 for bonding PLA together. Sand the side of the magnet you are gluing in and use Cyano Acrylate (super glue).

https://www.sciencedirect.com/book/edited-volume/9780815515814/handbook-of-plastics-joining pirate this and read chapter 17 it's really valuable

I actually prefer other kinds of fastening for pla. Magnets can be melted into undersized holes via a soldering iron (just avoid cooking too hot, keep it around 100 degrees).

Push fits and friction welds work well in certain applications.

I use the starbond brand 'super fast thin high performance super glue' and it works really well, but damn, you really don't want to get that on your fingers, it's a pain to remove.

I haven't used it on big prints, but for small models, tabletop terrain, and fixing miniatures it's been great.

I know this isn't strictly an answer to your question, but maybe something to consider:

I have a hot-air soldering station with different nozzle sizes, one of which is very small. It can be precisely controlled up to 480°C, and it's awesome to weld PLA or PETG together. I stopped using glue alltogether.

I've been told that methyl ethyl ketone is a good solvent for PLA (similar to acetone and ABS).

Acetone dissolves PLA. You can use it for chemical polishing but also for assembling parts.