Pages v8.1 was the last version available for macOS High Sierra (10.13.6). I am surprised that it still works on Tahoe, even with Rosetta 2. The latter will not be available with the release of macOS 28 in Fall 2027.
You should be using the current (e.g. 15.3.1) version of Pages on Tahoe with your 2024 Mac. It will open all prior Pages documents, provided they are undamaged as far back as Pages '05. What it won't do is seemlessy migrate auto-correction text replacements that you may have established in Pages v8.1 preferences, or any custom templates that you may have created that are located in Pages v8.1 My Templates. This is because they are entirely different applications now.
When you install the current version of Pages from the Mac App Store, it will install a separate application from your existing Pages v8.1, and with its own Settings. You should drag and drop that new Pages application icon to your Dock, as any existing one remains pointing to Pages v8.1. The icon will be visibly different.