How do I continue using my Intel-based iMac and Epson printer after support ends for Intel-based apps?

Your 24-inch iMac is an Apple-silicon Mac if it is a 2021-or-later model. 

The warning you received is about an Intel-based app or component running through Rosetta. 

Apple says Rosetta will continue to support Intel-based apps through macOS 27, with changes beginning in macOS 28. Apple — Using Intel-based apps on a Mac with Apple silicon

The good news is that Epson has specifically addressed this situation. 

Epson says that if you are running macOS 26, its drivers and applications will continue to work normally. 

Epson is also working on support for future versions of macOS and recommends checking the support page for your particular printer for updated software. Epson — macOS 26 Tahoe Support

So, with your iMac running macOS 26.5, there is currently no reason to stop using your Epson printer or avoid macOS 26 updates because of this warning. 

The thing to check before a future major macOS upgrade is whether Epson has released compatible software for your particular printer.

If you give us the exact Epson printer model number,

We maybe able to help and check Epson's current information for that model and tell you exactly what, if anything, you need to do before upgrading.

This is a user to user support site. Apple will not respond here.

It means that the next major operating system version release in about a year from now will no longer support apps that were written during the era of Intel mac computers. Your low ink reminder service contains Intel code and at the end of next year it will stop working. You options then will vary;

1) Hope that Epson brings out Silicon era code performing that service.

2) Learn to live without the service.

3) Don't upgrade your computer's operating system version any higher than macOS 27-something.

Even if you decide you can live without the reminder service, there could be other printer related services that at still hanging around and being used. Conceivably your printer could stop working with a Mac using macOS 28 entirely since the software will no longer work on the new system. That's possible if your printer is really old and Epson has stopped developing drivers for it.

This free app was developed the last time Apple's system software dropped support for a series of old applications and they include mention of the upcoming one next year. You can use it to preview any software you may be using that will stop working if you do decide to keep upgrading your Mac in step with what Apple would have you do. https://www.stclairsoft.com/Go64/

For now, nothing. If you later choose to upgrade to macOS 28 or beyond(not 27), check Epson's website for newer software.

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Which model Epson printer?

Whatever printer app from Epson is installed here seemingly hasn’t been updated in ~six years, and the app either needs an update, or the app needs replacement, or macOS needs a different path to the unspecified Epson printer, or this is headed for a replacement printer when you decide to upgrade to macOS 28 or later in a year or three.