I don't think an XM module can utilize VST effects and instruments
You don't seem to remember a lot from the pre-MPTM days, do you?

XMs can very well contain plugins but it is heavily discouraged, and in that sense you are right that for an XM file won't matter which version of OpenMPT is launched most of the time. Whether you use 32-bit or 64-bit OpenMPT really only makes a difference when you use VST plugins.
FWIW, the linked issue does not propose any specific solution to the problem, and I think "asking the user each time they click on a module file which version of OpenMPT they want to launch" is not a solution. But you can easily solve this issue yourself for the time being using RegEdit:
The path that you need is
HKEY_CLASSES_ROOT\OpenMPTFile\shell. There is an
Open folder in there, and you need another folder with exactly the same contents (but different name obviously). That other folder would then point to the "other" OpenMPT instance (i.e. if Open's command points to 32-bit, the new folder's command would point to 64-bit). Doing so adds a new option to the context menu of files associated to OpenMPT.
Even without that, right-clicking a module file will give you the "open with" menu, where you can choose between different OpenMPT executables, but they will be hard to tell apart because they will both have the same name.