I'll be honest: people more interested in fighting about specific game categorization than talking about the subject in general is really tiresome. So I will leave the thread to you folks so you can quibble without interruption.
It seems like the former informs people's thinking about the latter. Deciding whether I prefer bespoke or generic systems requires, to some extent or another, drawing on my experiences and understandings of games out there and how I categorize them.
There is also a certain degree of "othering" when it comes to how some non-mainstream games are relegated to "bespoke game" status while being similarly broad in scope as more mainstream games.
That said, I would look at video games for a definition of a "bespoke game."
Any video game that is developed especially for a particular person or sub-group of people that is not commercially available for the general public to buy in shops and commercial retail outlets.
I think that this is a more functional definition that provides some parameters, however vague in some places (i.e., particular person or sub-group of people). But it's worth noting here that this means that "bespoke" is not the polar opposite of "generic." "Bespoke" exists on a spectrum of commercial availability and target demographics.
If we apply this to TTRPGs, then I do think that we have a much better way to distinguish between bespoke and non-bespoke games.
Blades in the Dark, by such a definition, is
not a bespoke game. It is a commercially available product in stores. BitD is a pretty common sight in a lot of tabletop hobby stores, though it is less common to find in larger retailers, which usually only carry D&D, if they even have a tabletop roleplaying game. I even bought my copy of BitD from a small tabletop hobby shop here in Vienna.
However, there are a lot of bespoke games out there on itch.io, Kickstarter, BackerKit, DriveThruRPG, or elsewhere. You cannot find them in shops or commercial retail outlets. These games are clearly designed for particular sub-groups of people.