Private mission launches to extend life of out-of-gas communication satellites

Probably not, launch costs are still a few thousand to tens of thousands per kg so launching a 500kg jetpack vs a 5000kg satellite is pretty substantial.

Easier yes cheaper no, these satellites are in GEO.

Cost of per kilo to GEO is high. That is not going to change by enough even post starship level of 2 stage resuse - as GEO launches would need a third kicker stage as the second stage will not go so high to be reusable.

Also nobody wants to clutter GEO with many new sats. There are limited slots and dead satellites need to move graveyard orbits and cannot be de orbited[1]. The slots + frequencies are so limited that small pacific country of Tonga[2] makes millions every year renting this out.

Every final stage/booster that launched a GEO satellite is also in orbit now. Including the stage that launched this mission.

All this method basically reduces launched orbital objects from two (stage + sat) to just stage. The new sat/repair unit just attaches to older satellite .

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[1]In reasonable time frame that is, unlike in LEO, GEO reentry times can range between hundreds to thousands of years

[2] Due to quirk of international law they have rights to it. Like IP address allocation it was basically first come first serve for countries and one guy figured he coule exploit the loophole via small sovereign country .

If you really only need to send fuel, just do that. There's multiple fuel pods and a single robotic vehicle that goes around to each satellite to install the fuel pods. Sure, you're still launching a a big robotic vehicle but that vehicle will service multiple customers. It's cheaper for all of those customers to share the cost of one expensive satellite that to each pay for their own new one. The rest of the equipment on board works great, they have just gone past their expected service life (typically 15 years for GEO).

GEO communication satellites have become less attractive as worldwide internet access gets better (either fiber, mobile, or LEO constellations like Starlink) so it's hard to justify spending the money on a new 15 year mission when it's entirely possible you won't ever sell enough bandwidth to pay for it. It's way cheaper just to extend the life of existing assets so you can better guage if you actually should eventually replace it or exit the market.