Zoho Mail's free tier doesn't include IMAP (for new accounts since about 3 years ago), so you wouldn't be able to use Thunderbird, FairEmail, K-9 Mail, or other third-party apps. Offline access on the free tier is restricted to Zoho Mail's desktop and mobile apps. Zoho's Mail Lite plan ($1/user/month) does include IMAP access, and you'll need to do some calculations to see whether Purelymail or Zoho Mail is cheaper.

https://purelymail.com/advancedpricing

https://www.zoho.com/mail/zohomail-pricing.html