If you want to send mail from your custom domain from within Gmail, you need to use an SMTP relay like mailjet, mailgun, sendgrid, etc. Most have free tiers with high enough sending limits per month that are more than enough for personal use.

Once you have signed up and get your SMTP credentials, you can add it to Gmail like here: https://support.google.com/mail/answer/22370?hl=en#:~:text=Step 1%3A Add an address you own 1,username and password on that account. See More.

Your SMTP relay will also provide instructions to setup dkim/spf records with your dns.

If you don’t need a dedicated mailbox, just buy the domain from a provider like cloudflare or Google that supports email forwarding. Google forwards all emails to @mydomain to my Gmail account for free.

If you also need outgoing email, sign up for an SMTP relay. I use mailjet, and their free tier offers high enough limits for my personal use. Within Gmail, I added the SMTP settings from mailjet, and I can now send email from my custom email address by just selecting it in the compose page.