You may self-host services at home, but you need to think about the potential drawbacks for your privacy.
Let's explore what kind of information could be extracted from self-hosting, especially when you use a domain name.
A domain name must expose some information through WHOIS queries, basically who is the registrar responsible for it, and who could be contacted for technical or administration matters.
Almost every registrar will offer you feature to hide your personal information, you certainly not want to have your full name, full address and phone number exposed on a single WHOIS request.
You can perform a WHOIS request on the link below, directly managed by ICANN.
If you use TLS certificates for your services, and ACME (Let's Encrypt or alternatives), all the domains for which a certificate was emitted can easily be queried.
You can visit the following website, type a domain name, and you will immediately have a list of existing domain names.
In such situation, if you planned to keep a domain hidden by not sharing it with anyone, you got it wrong.
If you use a custom domain in your email, it is highly likely that you have some IT knowledge and that you are the only user of your email server.
Using this statement (IT person + only domain user), someone having access to your email address can quickly search for anything related to your domain and figure it is related to you.
Anywhere you connect, your public IP is known of the remote servers.
Some bored sysadmin could take a look at the IPs in their logs, and check if some public service is running on it, polling for secure services (HTTPS, IMAPS, SMTPS) will immediately give associated domain name on that IP, then they could search even further.
There are not many solutions to prevent this, unfortunately.
The public IP situation could be mitigated by either continuing hosting at home by renting a cheap server with a public IP and establish a VPN between the two and use the public IP of the server for your services, or to move your services to such remote server. This is an extract cost of course. When possible, you could expose the service over Tor hidden service or I2P if it works for your use case, you would not need to rent a server for this.
The TLS certificates names being public could be easily solved by generating self-signed certificates locally, and deal with it. Depending on your services, it may be just fine, but if you have strangers using the services, the fact to accept to trust the certificate on first use (TOFU) may appear dangerous. Some software fail to connect to self-signed certificates and do not offer a bypass...
Self-hosting at home can be practical for various reasons: reusing old hardware, better local throughput, high performance for cheap... but you need to be aware of potential privacy issues that could come with it.