When is a not updated software considered deprecated in the academic world?
I don't think there is such a standard, certainly not one applicable to all of academia. For your thesis, I would suggest that it might be more useful to talk about "recently updated" / "currently developed" software, rather than labeling the rest as obsolete.
"Deprecated" signals that the creator no longer recommends using the software. I can't think of any real examples for a full software package (i.e. going beyond deprecating part of an API), but I guess it might happen if the software is known to produce bad results.
Software might be "obsolete" if it has been de facto replaced by a better option, but certainly not just because it's old. Even then, the old option might be good enough. Visit a couple of (established) experimental labs in the sciences, and you'll likely see lots of old equipment still running old software. Changing it all out would just be needless overhead, and not be guaranteed to help. There's almost always a better place to spend the money you might have... From another angle, if you consider numerical algorithm implementations and libraries as tools, there's a number of them that have gone decades without updates, yet are still routinely imported and used in new software development.
The most common usage of "deprecated" is quite different and has nothing to do with the date of the last update. It means that the developer (or group) responsible for the overall system (Java libraries, say) has decided that in the future the feature may be dropped or modified so as to not be backward compatible. It is a promise about the possible future, not a statement about the past.
Somewhat related, an organization, usually a large one, can deprecate the use of a piece of software, meaning that they permit employees to continue using it for company projects, but will no longer provide IT support. But that is an individual company decision and could occur at any time.
Even your "obsolete" idea is flawed. It isn't about when it was last changed, but when it last was used for important work. Software can be regularly updated, but if no one cares, it is effectively obsolete.
Of course, you may reduce the number of tools you consider to suit yourself. But you should most likely focus on the most commonly used tools, rather than ones that haven't been updated for a while. After all, a stable release is valued if it is fit for purpose. If the problem space doesn't change, older tools may have a benefit. Likewise a tool built in a domain-specific language might be quite valuable to users, so excluding it arbitrarily might be a mistake.