In that case, a custom ROM is probably the best bet. I quite like GrapheneOS, as it will let you install Google Play but sandboxed - this gives you a lot more control to suppress its notifications (so your phone isn’t begging you for attention when it doesn’t really need it) while still keeping Signal and Telegram updated. I’m assuming you’re able to use hte phone without compulsively going to install things without parental controls to literally stop you, so the Play Store itself being available wouldn’t be so much an issue. The issue is that GrapheneOS is only on relatively recent Pixel phones only, and that’s a lot of money to spend on a device that only ever runs chat apps and phone calls. I don’t know of any other custom ROM that does that sandboxing, so I don’t know whether they’re able to suppress those notifcations which are likely at hte heart of any compulsive use.

I would say a flip phone would be better, but again since you specifically need these two apps that does limit you to a smartphone of some kind. Lively sells phones marketed to seniors (you might remember commercials for Jitterbug phones) that can be locked down with only a few apps - this might work for your purposes But if you do that, do at least make sure someone else gets your old phone that needs one, no sense in contributing to e-waste.