Will brand matter between a rear derailleur and front derailleur?

If the derailleur hanger is bent, it certainly does matter. It is a very common source of shifting problems, particularly after crashes. Even a small visible bend is bad.

No matter how good the derailleur itself is, if the hanger is bent, you won't get good shifting. It should be straightened using a dedicated tool (it can be done without in a coarse way, but not that well) or it can be replaced. The hangers are made to be replaced but can be frame-specific. If you cannot find a spare easily, take it to a bike shop and let it be replaced or straightened.

However, if your mechanic didn't notice the bent hanger, consider that it can be the case that either a) it is not bent after all, or b) the mechanic is not good enough and it is better to take your bike elsewhere.

To answer the title: No, the brand often does not matter between 7,8 and 9 speed rear derailleurs. Just keep the same number of speeds on the shifter and on the cassette. The exception may be some SRAM 1:1 groupsets, Campagnolo, Microshift Advent and some other. If it says Shimano compatible, it should be the same.

I believe you are referring to the shifter, not the front derailleur. The shifter connects to the derailleur with a cable

Sensah Reflex is an 8 speed system with components designed to be interchangeable with Shimano 8 /9 speed.

http://www.disraeligears.co.uk/Site/Sensah_Bicycle_Components_2020_page_6.html

Probably the Sora RD is slightly better quality, not because it is 9 speed but generally Shimano have better manufacturing standards and shifting quality than most other brands, though Sensah doesn't seem to be terrible at all.

There is no difference between an 8 speed and a 9 speed RD so that part is fine. (Often a 9 speed is a more expensive part and made from lighter materials , but that's all)

Given that you still have shifting problems and have identified that the derailleur hanger is bent, it is obvious that that is the source of your problem. So find a replacement derailleur hanger, keep your Sora RD. If you can't find a replacement hanger perhaps you can straighten it, but given your mechanic has failed to do so replacement seems a better option.

https://www.parktool.com/blog/repair-help/rear-derailleur-hanger-alignment

The bent derailleur hanger will undoubtedly give you shifting issues. The mechanic should be able to sort that out easily with a special alignment device.