Process model showing "Invalid Process" and no other error or logs.

I do not have a great answer to this. When I had this issue in the past, the fastest way to a working process was to rebuilt it.

But, did you try to load an older version and check whether that works?

Yes, I reverted to the older version and also tried importing the object from another environment where it's valid. However, the deployment was skipped with a message indicating no changes, so I assumed the main process was fine. I suspected the issue might lie within a subprocess or a referenced rule. I reviewed all subprocesses and rules, and everything appeared to be valid and functioning correctly. At this point, I have no clear indication of what went wrong.

The most likely issue is a referenced constant, expression rule, or subprocess that became invalid. Check recently modified constants/rules, look for deleted/renamed objects still referenced in the process, verify subprocess parameter mappings and permissions, and check for circular dependencies. We encountered similar issues previously and found the root cause was typically these dependency problems rather than the process model structure itself. When import shows “no changes” but the process remains invalid, the issue is almost always in a referenced object or subprocess configuration.​​​​​​​​​​​​​​​​

Give it a try…

I have seen this kind of issues resulting in a deep debugging of all the precedents. The cause can be an incorrect key word syntax for a precedent expression rule, e.g. deleting a rule input in an expression yet passing the input for that from the parent, having an expression like below in a precedent expression

a!localvariable(
local!varA: : "two colons instead of one",
{
rule!someRuleHere(
mapA:ri!mapA, /*map A doesnt exist anymore as its deleted yet its referenced*/
mapB:ri!mapB)})

Or, it can be related to some variables configuration in a script task in process that is not caught by syntax check of process model. To check this faster use the 'Generate Documentation' feature of process model. 
For rules involved you should check all the expressions and interfaces until you find a cause.