Agreed with @Cralamarre…AWS SES is a good option. Your out-of-the-box send rate quota is ridiculously low though so you need to make a AWS support request asking to bump up the quota in which case they will set it ridiculously high. They haven’t clued in to the fact that their SES defaults are set badly.
I also relay via Gmail but beware they have the strictest set of rules and a more complicated secure connection setup than other relays. You will likely have to go into Google developer and set the relay into insecure application mode to connect it to WordPress (see https://support.google.com/accounts/answer/6010255?hl=en).
I also relay via GoDaddy using their Workspace email. Don’t accidentally get sucked into the GoDaddy outlook 365 service…if you go that route you might as well go direct via Microsoft Cloud. GoDaddy workspace email is easiest to connect to of these three. Works fine. I have been using it for over a decade with no trouble. GoDaddy rumbles about phasing it out thought. Not sure why…it is actually one of the top emali providers by volume. GoDaddy Workspace free email (with domain purchase) does not support imap email clients (like Apple) so you will need the paid Workspace email if you are an Apple email client user. NOTE: This only affects you…the email administrator…not your clients.
NOTE: The advantage of Gmail / GoDaddy email relay is you can use the account for inbound email as well (like your website contact form). AWS SES has inbound email but it is not really accessible in a consumer-friendly fashion unless you have a workmail account to direct it to. So AWS Workmail is an option but it only supports iMap not pop3.