OP, don't be confused by an idea that if you get a 4K AppleTV, you must own a 4K TV... or that the latter must come before the former. Neither is true. Having MORE hardware capability to work with lessor other parts is no problem at all. A 4K AppleTV will render for a 1080p or 720p TV just fine. Better hardware will simply serve up maximum quality to lessor hardware.
In spite of not making direct use of the headline feature of the new generation, you'll also get far faster chips, up-to-date apps, HDR support, etc: all of many benefits that come with "latest & greatest." Your endangered/extinct App functionality problem will also be solved for the next few years.
Your Mac, Phone, iPad or similar are likely overkill (hardware) for your needs too. For example, if you own select Macs, yours may be able to output 8K resolution, but you probably do not have an 8K monitor. Most modern Macs have Thunderbolt 4 connections but few of us own much Thunderbolt 4-based supporting hardware (just about everything steps DOWN from full T4 capability to be used with that superior hardware): most commonly, T4 to Hub, which then lets up to everything else connect with inferior (to T4) connections.
You probably rarely- if ever- tax any the Apple hardware you own. And yet, you probably own such hardware anyway. Why? Because "the rest" is part of the value and if some parts of them have capabilities beyond what you can use today, that's OK- maybe you'll use/need them tomorrow.
If you buy a 4K AppleTV today, your next TV will probably be 4K (the 1080p option is fading fast at retailers). But even if a <4K television outlasts it, the rest of what it can do will bring great value... WHILE maximizing for the TV you already own.