If TfGM were part-funding the X5 then this funding contract will always have had an end date. I would expect that this end date for funding would have coincided with the start of Bee Network tranche 3. So yes, the funding will always have been time-limited and, yes, this funding will have been designed to tide things over until the start of Bee Network.
As for the minutiae of the other changes, buses going from hourly to 2-hourly is certainly not ideal but we're talking about a sparsely populated and affluent part of Trafford. One must presume the demand wasn't there for much more. Beyond that, it looks like a couple of roads lose their buses but that alternative buses are available within half a mile.
Cross-boundary services are always going to be an issue when there is franchising. With the way s.123 Bus Services Act 2017 is written, I'm not convinced it would actually be lawful for TfGM to tender a service which operates inside the franchising area but put it out to tender separate to and outside of the franchising scheme. I'm sure other posters will be more familiar with the legislation and will correct me if I've misunderstood the legislation.
The 5/X5 is an edge case (probably the only edge case) where it was operating as a tendered extension/enhancement to the standard daytime service which operates commercially and that the service is operated from outside of the franchised area.
Other services in a similar position are either operated fully commercially from outside the area (e.g. X43), are operated by a Bee Network franchisee (e.g. 184, 100), or are not funded by a TfGM tender (e.g. 111, which is a Lancashire County Council tender). I don't see that you can blame TfGM for any of this. You can see why Warrington's Own Buses wouldn't want to give up the commercial bit and have the whole of the X5 as a Bee Network route, why Warrington couldn't/wouldn't fund the non-commercial bit outside of their boundary, and why TfGM couldn't fund it as it's outside of Bee Network. The only real possible compromise I can see is what we have: the 5 continues to run commercially during the daytime, the evening service disappears without TfGM funding, and we have a Bee Network stump from Altrincham to Lymm.