There's a fine line between good service and "necessary" service. A good server is right there anticipating your needs and that "Can I get you anything?" is "What's next?" carefully timed to be at hand just as you finish the current drink so there's no lag between drinks. That server is doing a complex calculus of your drinking speed and the current bar's speed and trying to ask at the right moment that they can "just about read your mind", collect your next order, finish it in the right order at the bar and deliver just moments before you need it.

The "necessary" service is indeed hopefully trying to do all of that, but also has to add in the calculus of the business needs and try to send polite messages when they think turning over the table entirely is better for business. Keep in mind, that isn't always the case: a higher tip on a few more (higher margin) drinks is just as useful to the business sometimes as the turnover time just to end up with someone ordering just lower margin foods and giving a bad tip.

I have found that if you are curious if you are getting the "good" service or the "necessary" service in that moment, it's easiest and best to ask. They may feel too polite to say something unprompted, but they are almost always happy to answer direct questions if you are kind about how you ask (and if you can give an apology if you find out that you have taken too much time). I've found that asking also sometimes opens up interesting responses. Again, keep in mind that a good tip on a "slow drinker" can always be a "bird in the hand" that a server doesn't want to waste on a possible "two in the bush". I've been invited/welcomed to take a conversation (or my book in cases of dining alone) to a bar or a lower revenue table before (maybe one with less of "a view" or a smaller size). I've been asked to tip out a server switching shifts, with no need to close the full tab, and then treated generously by the incoming server for saving them end of shift math and making their coworker happy. I've had appetizers or drinks entirely comped just because I was nice enough to ask if the server needed the table, apologized for the inconvenience to them, and the server hoped I'd return during a less busy shift.

I don't think it is my problem to pick up "hints" when servers are being too polite, and I'm not the one paid to do the calculus of what's best for the customer (me) versus what is best for the business. I try my best to present as the best "bird in the hand" that I can so that a server is never resentful of me taking up their service at the expense of whatever line may or may not exist. The line is of no concern to me. One of the ways to present as a good "bird in the hand" is to ask if I'm taking too much time, drinking too slow, and then no matter the response I get back, I know that I should be appreciative of whatever the response. Sometimes the response is truly "you are fine, take your time" (which is perhaps the one hardest skill, because of course you will get that a lot when servers think they need to be polite, versus when that is the real answer), and when that it the real answer I always deeply appreciate that. It can be nice to feel recognized that you are a good customer and the server knows they have a good "bird in the hand" and doesn't want to waste the opportunity. I always try to appreciate that (especially when you know there is a line of envious birds in the bush).

(ETA: I nearly forgot possibly the best advice I've picked up over the years: depending on the type of restaurant, the best person to ask what the expected turnover time for a table is almost always the Host. They get tipped indirectly from the servers so they have even fewer reasons to give polite answers rather than real answers. It's directly their job to manage the balancing act of turnovers and lines/waiting lists/reservations. Often you can ask before you are even seated and get a great approximation so that you can appropriately pace yourself. I've also asked them sometimes, when I arrived during a slow time on the sort of night where I expect that to change abruptly, to let me know if anything changes and they find a need to turnover the table "soon" and have won brownie points with restaurants that way as well. You also get a great feel for a restaurant asking the Host questions about expected turnover. You'd sometimes be surprised how many restaurants have expected turnovers closer to four hours than the one and a half most people think of a "meal time", what that says about how they try to pace the meals themselves, including after dinner drinks, and sometimes what that says about their margins and business model. A good restaurant may not need fast turnovers, it may be more than happy with slow ones.)