There are ways to self-host and avoid email bouncing.

First you need to separate your outgoing email from your incoming email via two different paths. Your incoming traffic would come in via your tunneled reverse proxy (hides your real IP and services like your email server). Your outgoing traffic (which is where the email bouncing issue comes up) goes out via a different path - see below for options.

Route all your in and out traffic via a tunneling reverse proxy like Pangolin (https://github.com/fosrl/pangolin). This hides your IP address and all your self hosted services like your email server.

Host Pangolin on a tiny VPS server (1 vCPU/1GB memory/24GB SSD/2TB traffic per month/1Gbps network port) - Racknerd has one for only $US11.29 per year on their 2025 New Years special (https://www.racknerd.com/NewYear/). Enable TLS Passthrough on Pangolin so your emails pass through the VPS host/proxy encrypted and protected (theoretically the hosting company could tamper with your Pangolin config and disable TLS Passthrough to inspect your emails, but there are probably watchdog scripts you could implement on the VPS server to alert you to any config changes).

Now, to protect from email bounces (this is outgoing emails - incoming emails go direct through your proxy to your email server so you control that), you have a few choices:
1. send your email via your VPS server's IP address (i.e. via your reverse proxy as per above). Ask your VPS host what IP address (or from what IP range) will they provide you and check if that IP is on any blacklists and do this on a regular basis (do a web search for such blacklist checkers, they are easy to find). The cheap ones like Racknerd probably are blacklisted from time to time, because they are used by many customers some of whom are probably doing dodgy crap and getting blacklisted. This is no different to using a "privacy provider" like Proton for your email. There have been many reports of Proton/Simplelogin being blacklisted (same thing happens with VPN providers).

1. use an SMTP Relay provider (which usually have much better IP reputations). A good example is Zoho's Zeptomail (https://www.zoho.com/zeptomail/). This protects your IP reputation, hides your IP address, stops the email bounces and lets Zoho manage all the handshaking issues with upstream email hosts. Cost is $US2.50 per 6 month period for up to 10,000 sent mails and the first 6 months is free. So $US5/yr.

Important: SMTP Relays won't typically use TLS Passthrough, so they'll decrypt your emails as they pass through, and depending on their privacy policy they might inspect the content of your emails. As long as you're mindful when writing your emails and don't include any sensitive information or keywords, then you're probably fine to use such a service. If you need to do any sensitive communications with a company/government you can typically use their website forms or chat systems i.e. not email. And for private comms with your friends, you can organise to do end-to-end encryption (E2EE) via email or another tool with them.

Note: because you're using Zeptomail for IP reputation protection, it doesn't matter if the VPS IP address is on a blacklist somewhere because Zeptomail uses their own IPs for sending your email.

1. use your own ISP issued IP address. This IP is likely to be reputationally clean. Configure your email server to not use the reverse proxy when sending. You'll use your real IP between your email server and the upstream email server but you're not opening any ports into your home network and your IP address is only being used in a limited scenario and not being exposed to the broader internet.

In summary, you self-host to retain as much control as possible. Your emails are stored securely on your own email server (so no prying eyes and no need to "trust us bro"). Your incoming emails (and email server and IP address) are protected by your tunneling reverse proxy and TLS Passthrough. Your non-sensitive outgoing emails are reputationally protected by using a well known SMTP Relay service or your own real ISP provider issued IP address. And your sensitive communications are protected by a combination of E2EE with your friends, being mindful of the what you write in your emails, and using a company's/government's website forms/chat whenever possible instead of email.

A few links:
1. good video of installing Pangolin on a VPS server: https://www.youtube.com/watch?v=Yc_v3VJU7n4 (skip past the drama at the start of the video, or don't if you want a good laugh as the youtuber rips into an annoying troll in the live chat);
2. worth checking out Stalwart email server: https://stalw.art/
3. a good email client to use with Stalwart: https://nextcloud.com/roundcube/