Besides all the marketing fluff - are there "better" rechargeable
batteries for these low-drain scenarios, e.g. Eneloop? Better: keeping
their charge longer.
Yes. Cheap NiMH batteries generally have high leakage and go flat within a few months. LSD (Low Self Discharge) batteries such as Eneloop may hold 90% charge in 1 year and 70% after 5 years.
I use Eneloops in all my devices, including electric clocks and instruments that are rarely used. They recharge in about 1.5 hours, but I keep a few charged spares on hand so I don't have to wait. I prefer this to buying 'dry' cells even though they may last longer in low drain applications, because:-
Having to make a special trip to town just to buy a battery is a pain.
They are much more expensive when total usage is considered.
They are usually sold in packs with more than I need, but perhaps not enough to make a complete set (and then I have to buy another pack just to get 1 more cell!).
You never know how much charge they actually have.
is there a benefit in using these for the TV remote? Do they last
longer?
Theoretically an Alkaline (not 'Zinc-Carbon') cell should last longer than LSD in very low drain applications. But there may not be that much in it. At lygate-info.dk some batteries were tested at low current drain. A Duracell Plus Power AA discharged at 5 mA to 1.2 V got 2313 mAh, while an Eneloop 3UTGA AA got 1787 mAh, so the Alkaline only lasted 30% longer. But that was a top quality brand. Cheap Alkalines have no stated capacity and cannot be expected to last as long.
The big problem with primary cells is that you have to destroy them to measure capacity, so you never know what an individual cell is capable of until after it is used up. Cheap brands are likely to have lower capacity in general, but also more 'duds' that cannot be weeded out in testing. So you have to accept that those 'new' cells you just put into a device may not last as long as you expect.
Another reason for using rechargables is that 'dry' cells have a tendency to leak corrosive liquid when fully discharged, which can destroy the device they are in. This often occurs in devices which normally run on mains power, as the forgotten dry cells eventually go flat and leak even though they were never used.