Can Proton run an obscure Windows 98 point-and-click game?

Maybe, but there isn't enough information here to say whether Omnia Jr. works. Proton is worth a try if it's a Windows program. Add the installer or game executable to Steam as a non-Steam game, enable a Proton version in its compatibility settings, and see what happens.

If it installs but won't launch, check that Steam is pointing to the installed game executable rather than the installer. You could also check whether Lutris has an installer script for the title. There may not be one for something this obscure.

Wine is another option if Proton doesn't cooperate. For an old Windows title, trying a separate 32-bit Wine prefix is a reasonable next step. That keeps its configuration apart from other software while you troubleshoot.

The game might depend on old media components for its videos, or on copy protection that doesn't work properly. If it fails during a cutscene or asks for the disc unexpectedly, those are useful clues, though neither issue is guaranteed here.

First check what kind of program is actually on the disc. If it's a DOS game rather than a Windows one, DOSBox Staging is a better place to start. Being sold around the Windows 98 era doesn't necessarily tell you which it needs.

ScummVM is worth checking too. It supports a range of point-and-click games, but that doesn't mean it supports every one of them. Check its compatibility list for Omnia Jr. before spending time setting it up.