Workaround for downloading apps on 2010 27-inch iMac

If the applications in question require something newer than High Sierra, no. You won't be able to run them on that Mac.

In some cases, there may be alternatives. Even those are becoming fewer and further between.

• The current version of Safari requires Sonoma or later (soon to be Sequoia or later), and current versions of most third-party Web browsers require Monterey or later. Even the current version of Firefox requires Catalina or later. However, there is an old version of Firefox (Firefox 115 ESR) that has gotten multiple "stays of execution" – and is still on Mozilla's list to receive "critical security updates" for a few months longer. (Mozilla Support – Firefox users on macOS 10.12, 10.13 and 10.14 moving to Extended Support Release)
• The current version of LibreOffice requires Big Sur or later, but there is an archive of old, unsupported versions – including some that run on High Sierra (The Document Foundation Wiki – Documentation/System Requirements).
• The situation is bleaker when it comes to photo editors. The commercial program GraphicConverter 12 (available from the App Store or the developer's Web site) is probably the main one left. (The versions of Adobe Photoshop & Photoshop Elements and of Affinity Photo that were compatible with High Sierra are all discontinued, and even the current version of the GNU Image Processing Program (GIMP) requires Big Sur or later.)

Realistically, that iMac is mainly useful for running applications you already have, running old 32-bit games that will not run under Catalina or later, and connecting to FireWire gear (especially MiniDV and Digital8 camcorders). Also for running old Mac OS X / PowerPC applications under Rosetta 1 when dual-booted into Snow Leopard. Too many developers (including Open Source developers) have moved on to make it useful as a platform for running current applications.

Note that there's a good chance that iMessages and FaceTime will not work on that machine after January of 2027. There's a security certificate that expires about then, and I believe that Apple has issued patches all the way back as far as iOS 12 (on iPhones) and macOS 10.15 (Catalina) (on Macs). If there has been a patch for anything before Catalina, I'm unaware of it.

I suppose you could install a virtual machine program on that old Mac (if you can find one compatible with it), and then install a Linux distribution inside of the virtual machine. That would be easier than installing Linux directly on the "bare metal".