For stuff at the scale of a small Access database, does the normalization (or lack of) end up being a big deal?

I get that there are real advantages, I'm just wondering out loud whether they are universally applicable/important to small scale databases.

Speaking as someone with direct experience maintaining Access databases that should have been SQL Server from inception, yes it absolutely does. If you need to force feed 10+GB through Access artificial 2GB constraint and your programming language (VBA) is both single threaded and interpreted, if you aren't clever then you will run into performance problems, just as you would if you were doing something similar in Javascript or Python + SQLite.

I'm imagining a few hundred thousand small records when I say small, not 10 GB.

Probably matters as it relates to data quality mostly

That's a good question. For an honest and complete answer, I'd have to remember the messes I've seen and it's been a couple decades now, so I don't. But simply, everything in setting up forms and reports is more convenient if you have real relations as opposed to a bunch of columns like "supplier1, supplier2, supplier3...".