Well I think this is a bad example in general, because unlike most businesses, success is actually a zero sum game in top flight sports. If somebody does good enough to earn a seat, it will always mean that somebody else did bad enough to lose theirs. It’s also not a very faithful characterization of Mercedes. They were seriously considering letting Bottas go last year, it was honestly a surprise that they kept him (and let Ocon go instead).
If you want to see what the same management style looks like with competitive drivers, you can just look at the last time Mercedes had two competitive drivers. That would be in 2016, when Nico Rosberg won the drivers championship with Mercedes. The relationship between Hamilton and Rosberg had become so toxic, that Toto Wolf himself admitted he had no idea how he was going to solve it. It culminated with Hamilton trying his best to hold up Rosberg in traffic in the last race of 2016, because Hamilton needed to keep Rosberg of the Podium if he was going to get the title. You can watch the highlights on YouTube with the team telling him to speed up, while he more or less just refused. The only reason any of that was resolved, was because Rosberg retired after that season.
This story is pretty much repeated in F1 history any time you have two people on the same team competing for the title. Last year LeClerc and Vettel fought so much, and so dangerously on track, that it actually led to both Ferrari drivers crashing into each other and retiring in one race (something which mirrors one of the most controversial crashes in F1 history, when one McLaren teammate crashed into the other at Suzuka in 1989). The entire season was also full of their drivers arguing on the radio about team orders. Then you have the other most dominant driver, Verstappen, who Redbull have been unable to find a suitable teammate for.
To specifically answer your questions, at Mercedes “win as a team” clearly always means “help Hamilton win”. It’s not possible to operate a team where drivers are not fighting for their seat, and history has shown it’s not possible to have a good team culture when both drivers are actually competing with each other for the title.