No "standard" as such, every manufacturer uses different strings on the instruments they release.
Looking over other manufacturers, for 34"-scale solid-body fretted basses in standard tuning they do mostly seem to stick with the .045", .065", .080", .100" and .045", .065", .085", .105" string sizes that Fender favours. D'Addario refers to them as "Light" and "Custom Light" or "Light Top/Med Bottom" respectively: I'll say 45/105 and 45/100 here.
Yamaha,
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Invalid Link Removed are 45/105; Ibanez seems to be largely 45/105 with at least one 45/100 in the range at the moment; Warwicks are mostly 45/105 too. The Ernie Ball Music Mans all seem to be 45/100. The current Gibson
Thunderbird and
SG basses are 45/105 while the
Les Paul bass is 45/100. I'm not sure what's up with Aria. Rickenbacker basses come with very different string sizes but then they have a non-standard scale length as well. The biggest exception I've seen so far is Alembic, which puts a
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Invalid Link Removed shipping with 0.045", 0.065", 0.085", 0.100" at the moment.)
As you say, what ships as a manufacturer standard isn't a sure guide to what has a significant following among players. Still, it's probably a fair sign that there's at least a large constituency for those pretty-standard sets, between the people who actively expect a new bass to come with them, and the people who will just be happy to stick with them when the time comes to restring.