I hope you made backups before you started? In case it all goes a bit weird…
Good to see you are working in small batches so you can check them as you go along.
Picard WILL make mistakes and it is you the human who needs to correct the errors. Using that “lookup in Browser” and the < tagger > button to select the relevant releases. Then drag the track onto the correct matches.
The mistakes will happen more if you don’t have anything in the tags. AcoustID “Scan” does well, but often matches to the wrong compilation album
If you have a batch of tracks where your file names are good, but the tags are bad, then MP3TAG can often help there. It is pretty good at converting patterns of filenames into tags. This can then be used to better initialise your files with basic tags, and the pass to Picard for full tagging.
Have a look at this thread where I helped someone do exactly that with MP3 Tag.
And yes, this is hard work untangling a mass of odd tagging on 5000 files, but with patience it will be worth it in the end.