To my mind when I interview people there are two types of people who match what you've described:
1) I'm a generalist and go wide but only surface deep.
2) I'm a specialist in multiple areas, I go deep and because I know how to do that I have done it multiple times and can also do it for whatever your problem domain is.
The first of these feels more like your full-stack web developer and the lack of depth usually deter me from hiring... the latter though, the latter feels like an interdisciplinary master that I would want to hire so long as I can see that the candidate is able to apply that to solve our business needs within a month or two of ramp-up.
I haven't seen your CV but I'd make sure that #2 was obvious at the top of the CV as that would provide context to the roles on the CV, each one enriching who you are.
3) I'm a generalist problem solver with expert programming ability, who can adapt to any technology/stack and go deep with your problem domain as I've done multiple times across various fields.
IMO that seems like the ideal hire for any position, as they'd be good for existing problems, and they'd be good for any new problems the business might encounter. Rather than hire an expert in new technology X who knows nothing about your business and existing tech/infrastructure, you can throw Mr. 3 at it.
The only time I don't think that type of candidate would be useful is if the company is competing on technology, and they need someone who has dedicated their career to being an expert and/or researcher in that single specialty (example: machine learning). But even then, most companies don't need someone like that, and those that do could probably benefit from having some 3s on the team in addition to the specialists.
I like this, reminds me of a recent article from harvard business review about generalist. Something along the lines that generalists were better at making connections across domains and can come up with promising solutions to problems.
1) I'm a generalist and go wide but only surface deep.
2) I'm a specialist in multiple areas, I go deep and because I know how to do that I have done it multiple times and can also do it for whatever your problem domain is.
The first of these feels more like your full-stack web developer and the lack of depth usually deter me from hiring... the latter though, the latter feels like an interdisciplinary master that I would want to hire so long as I can see that the candidate is able to apply that to solve our business needs within a month or two of ramp-up.
I haven't seen your CV but I'd make sure that #2 was obvious at the top of the CV as that would provide context to the roles on the CV, each one enriching who you are.