Apparently, Minecraft Forge won't work with Game Pass. Whenever I try double-clicking the 1.7.10 installer, it does nothing except produce a log file showing a bunch of errors, even though I already launched Minecraft: Java Edition through Game Pass and even created a new world.
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Sadly at this point in time, Game Pass users can't mod their Minecraft because the game files are inaccessible. At some point Microsoft plans to allow Game Pass files to be moved around, making it possible to mod again. A lot of things have been messing up for me ever since Microsoft bought Minecraft and moved it to their store.