The state of email is disappointing and sad. It is possibly one of the most centralized decentralized protocols/networks on the planet. We need a good replacement for it. It's so legacy.
If you have set up a new system without any reputation now, even if you have set up DKIM and SPF, it's now a lot worse. Major providers like Google and Microsoft won't really tell you, but if you are new but don't have a dedicated AS and instead you're using (for example) Linode you'll be scored lower by having low-cost solutions that just so happens to be abused by spammers.
Still - if you self-host just assume at some point it will go down and you may have to deal with a backup restore before you can receive any more email. If that gets in the way of your life, you may want to reconsider :)
So, what can I do to just keep a backup of all my emails (one @gmail.com and other personal website emails)?
Maybe for me, just having those emails accessible somewhere is more important (other than primary source/ provider)
Thanks
Source: Having own email server for 17 years. Absolutely happy with it. Again, that doesn't mean everyone should do it, but I'd abstain from advices like you should not! or should do same.
I do host mail for tens of domains and never had issues with deliverability.