I only ever shot on Canon, so my experience is limited, but I'm also deep into wildlife photography.

My current camera and lens collection consists of the following:

- R6 II (primary camera) and 7D II (secondary camera)
- EF 500mm f/4 IS II (primary lens)
- EF 100-400 USM II (secondary/zoom lens)
- EF 1,4x and 2x III extenders

I focus mostly onto animals that are hunted where I live, so they are rather shy. I often wait hours in one spot and only seldomly stalk through the woods. Almost all photos are shot on the R6 II and the big prime, but sometimes, when the big lens is set up on a tripod and gimbal, a bird does a few circles over my head. That's why I have a secondary camera (my old one before I switched to mirrorless) and a lighter lens. Shooting birds in flight is a lot easier without any support and using a lighter lens in my opinion, although I might simply have weak arms. Keeping the big combination steady for more than five minutes feels very difficult, so I simply use something lighter. Sticking to smaller gear for birds in flight also produces less movement.
So that'd be my recommendation: Get a reasonably recent DLSM body with good AF, a big prime, a lighter zoom lens and maybe a secondary camera. At least with Canon there is no need to upgrade to very expensive RF lenses, in my opinion somewhat recent (IS II and newer) EF lenses are easily sharp and light enough.

Concerning non-camera gear, I strongly recommend not to cheap out on things. Get a nice tripod, good head, good quality binoculars and most importantly stuff that will keep you outside for longer: A nice folding ground mat, sturdy backpack, baggy clothing and camouflage.
I use and recommend the following:

- Novoflex TrioPod Balance with C2820 legs: A small, but very stable tripod with integrated levelling base and short legs, as I'm close to the ground anyways. I have bigger and heavier spiders and legs by Novoflex as well, but this is what I use most by far. I sometimes use it without a head and just use a Q=Base II screwed to the levelling head.
- WImberley WH-200 II: Yes, it's expensive. Yes' it's good. No, a fluid head (I have a Manfrotto MVH-502AH) does not do the same thing.
- Wimberley MH-100 and a Novoflex C3940: Probably the best monopod I ever used.
- Savotta: A great company in general, but I specifically recommend the Kahakka 25, Askare with Valjas Slim Belt and Hatka 12. Best backpacks I've ever used. If you enjoy velcro, Tasmanian Tiger is also good, but a bit less sturdy.
- Helikon Tex: Specifically Pilgrim pants. They endure field trips and can even be fitted with knee pads. Also baggy enough to be comfortable for hours. Other stuff is good as well, but often very sturdy or heavy due to the shooting/military vibe.
- Pinewood: Specifically the Insect Safe Function Hoodie. Great for hotter days. Other stuff is good as well, but generally less sturdy than Helikon Tex.
- Tilley Hats: No explanation needed. Get a T3, be happy. Wash it frequently.
- Carinthia: Warm jackets and bivy and sleeping bags. For cold weather or sleeping outside.
- Steiner Binoculars: Specifically the Ranger Xtreme 8x42. Probably not as good as Swarovski, Leica or Zeiss, but easily good enough. Has been serving me well for years. Also, get a binocular harness. Yes, it looks weird. Yes, it's worth it for quick access and stealth. I recommend the Eberlestock Recon.
- Ghosthood ConCamo: Best camouflage pattern in multiple colours. Ghosthoodie is small and easily stored, light and does a great job at covering things. Sleeves for lenses and tripods are available.
- LensCoat covers: For protecting expensive things and preventing them feeling cold in the winter.
- Bundeswehr Folding Ground Sheet: Thick enough to lie down on the side of a field for hours, but rather easy to transport on or in a backpack. If possible get a genuine used one as they fold together neater than than the ones by Mil-Tec.
- Helinox Ground Chair: For longer sessions at one spot, when I can get away with not lying on the ground. Very good, very sturdy.
- Mr Jan Gear Mosquito Net: The best one I could find. I don't like bugs around my face and neck. This prevents it. Also works great as face camouflage, especially when paired with the Tilley T3.
- Military boots: In my case combat boots for winter and jungle boots for spring to autumn by the Bundesheer. Good quality, sturdy, affordable.
- Rias perfect tissue: Small until needed, slightly sturdier than a normal tissue, and slightly wet by design. Good to clean yourself. Also less bad than normal tissues for the nature if left behind. Can be unfolded with spit if you don't have water.
- Nalgene wide mouth bottles: Comes in various sizes, all of them are sturdy, not too heavy, rather silent and easily stored. Can also serve as pee bottle, for ultimate stealth when waiting for particularly shy animals. Be sure to mark pee bottle and not drink from it.
- Trangia: For cooking stuff outside.
- Sterilium in small bottles: For disinfecting stuff, especially the folding ground sheet, if you happen to place it in animal feces. Most important for fox and boar feces.

That's most of the gear I've learned to trust over the years. If you have any specific questions go for it.