A phone with just calls, SMS, Signal and Telegram?
I want a phone where I can't go on the internet or read the news, just communicate with people I actually know in real life. Is there any way I can make this happen?
Might be easier to give advice if you can explain the motivation. Are you worried about privacy with smartphones? The cost? Spending too much time dicking around on it? Controlling a kid?
I don't know of a way to get a phone that only has those apps, they require internet to work. GrapheneOS can be quite secure and you can simply not install any more than the base apps and then freeze the built in browser, but then you'll need to manually update Signal and Telegram and I assume you needing to unfreeze your browser to grab regular updates is far too much of a pain. Running outdated versions of secure chat apps is a risk.
It's to have a less compulsive relationship to my phone. What I ended up doing was setting a 5 minuet timer on Chrome, setting it to black and white, and switching to a text-only UI.
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.
Ypu could buy a raspberry pi and attach a sim card module, then just not install any browsers. I think both signal and telegram needs electron but I think you can install electron without an actual browser.
I have been using the app "Lock Me Out". For your use case, you could make a list of allowed apps - Phone, your SMS app, Signal, Telegram - and set a 24h restriction to only those apps. Then password-lock it so you aren't tempted to remove the restrictions.