Linguistically, it’s a mood but it is presented as a “tense” in the
traditional fl teaching paradigms. That’s my view. However, in looking over
3 dictionaries of linguistics, we get a more complex and more nuanced view,
viz. modal or aspectual interpretations are used in analyses of English
while the traditional grammar treatment calls it a tense.
Another states boldly that semantically it is a mood but behaves like a
tense, esp. in reference to the Romance languages and another says straight
out that it is a mood.
All definitions cite the Romance languages as notable for their “conditional
tense” in traditional terms, but I know Russian has such and so does Urdu.
What marks the Romance seems to be the elaborate morphology of the
conditional whereas Russian simply uses a particle with a past tense form.
Urdu has a set of distinctive endings for the conditional but not as
elaborate as the Romance family’s.
For summer beach reading you might consider the Cambridge Textbooks in
Linguistics series: “Tense” and “Aspect”, both by Comrie and “Mood and
Modality” by Palmer. Maybe I’ll read them and then I’ll really know what I’m
talking about. Note that in current terminology in “traditional” Latin
textbooks, the infinitive is not a mood, but in traditional Roman usage, it
was considered a mood.
So things change.