Kodachrome
https://search.worldcat.org/ is a good inter-library search site. My librarians use it (among other things, I’m sure) to find books/DVDs to acquire for me on ILL, but since the site is public sometimes I just do the search for them and send them a link to what I want when I submit a hold request.
Your boundaries on cost make it tough, but aside from Tuta you might have a look at mail.ee which has very basic features (no E2EE for example) and a retro web UI, but very high storage limits. They offer free accounts too, and support SMTP/IMAP/POP3. It’s Latvian-based so comes with the “100% GDPR compliance” feature if that’s of interest.
Zoho.com is another that comes to mind. It’s very feature-heavy/slick (you can tell they’re attempting to market mainly to small businesses looking for a cheaper Google Workspace), has been around a long time and I’ve read positive comments from others about the service. It’s an Indian company though so you don’t get GDPR protections (or similar) as far as I know. The low-end plans are in your price range and I think they still offer a free plan - that’s what I have anyway.
I’ve been a Fastmail customer for decades now and it’s exactly what I want a mail service to be, but it’s out of your price range and has no free tier.
The Fediverse needs an r/fatlogic analog, made entirely of stretchy materials of course, where this kind of Fat Acceptance garbage can be posted. It’s a special flavor of mildlyinfuriating, Now with 200% of the calories, but don’t worry, it’s healthy … of course it is!
The Thunderbird desktop mail client is far better (feature-rich, stable, interoperable) than any webmail or phone app mail client I’ve ever seen.