I know you said no services but I didn’t really find any SMS apps that I enjoyed and found more satisfaction with an alternative service so I’ll detail that below for anyone curious. My favorite of the regular SMS apps had to be QKSMS though - nice customization options and it has message scheduling.

If you’re looking for a higher level of privacy (the most you’ve get with an insecure protocol like SMS at least), I’d check out porting your number to https://jmp.chat/ with https://cheogram.com/ as a VOIP number. You save a lot of money and at least after initial setup, you don’t have to stick to Cheogram as your XMPP app - I switched to Monocles which is still open source and available on F-Droid and all of my VOIP numbers still work fine. Same said for desktop - I use Dino and have access to all of my texts right on desktop.

Then you can just use a data only SIM on your device to stay in touch when you’re out and about if you’d like. That SIM still has to drawbacks of basically being connected to your identity through your IMEI but at least presumably most of the time while you are connected to WiFi, you have the option of disabling the SIM if you’d like and be able to use your phone number without giving your location data to your carrier. I choose to keep airplane mode on all the time and just have the data only sim for emergencies. If you want to go harder, jmp also accepts cryptocurrency as well as some data only SIM providers such as https://silent.link/ so you could completely use decentralized currency to pay for your phone service which is kind of cool.

I believe it is possible to self host the XMP server that is interfacing with your SMS number as well but at the end of the day SMS is already basically cleartext across the network with how many eyes are on it so I felt comfortable just trusting the servers they provide as part of the subscription.