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Authy got hacked, and 33 million user phone numbers were stolen
(appleinsider.com)
This is a most excellent place for technology news and articles.
Whoa there, I never have - and never would - suggest that anything should be protected by a single factor. Where are you getting that?
Authy sucks. It's not just that the TOTP they send you might not be secure (SMS is easily exploited), it's been shown that they're leaking other personal data.
You don't have to cobble anything together. As you say, self-hosted BitWarden is a good option. As for your "glue", you should trust it more than a third party, since you know what went into yours, and its not a massive ~~honeypot~~ treasure trove.
Edit: I've been using "honeypot" wrong. It would actually be good if the hackers tried to hack one of those.