What you see
The symptoms are fluid dripping near the electrical connector, fluid wicking into the connector or the wiring, and transmission faults or limp mode. The cars are ZF 6HP automatics: the E9x 3 Series, E60 5 Series, E70 X5 and others. See Transmission Mechatronic Sleeve (ZF 6HP), BMW E90 repair costs and BMW E60 repair costs.
Why the bill is not the sleeve
The note says the sleeve itself is a cheap part, and that labor and fluid make up most of the bill. Both owner reports on the page include the sleeve plus a pan, filter and fluid. The parts list names ZF Lifeguard 6 fluid. Transmission Mechatronic Sleeve (ZF 6HP) on a BMW E90/E92/E60/E70 and similar models typically costs $550–$733 at an independent shop, based on 2 real owner-reported prices.
Do not jump to a transmission
The automatic transmission page says to get a pan drop and a diagnosis first, because many "failed" transmissions are a mechatronic or fluid issue. Slipping, no reverse, or limp mode can be that larger job, but the sleeve leak is the connector-area drip. See Automatic Transmission Replacement. The 8-speed fluid service is a different gearbox (ZF 8HP Transmission Fluid Service) and is part of the mileage discussion in the BMW 60,000 and 100,000 Mile Service Costs.
Fluid service context
Whether BMW automatic fluid is a "lifetime" fill, and what owners paid to service the 8-speed and the 6-speed, is the BMW "Lifetime" Transmission Fluid: Should You Service It?. This page is only the leaking connector sleeve on the 6-speed.