Not a sermon, just a thought. When I went to Tanzania, here's what I did for my Canon with an 18-400 lens from Tamron. I used shutter speed priority (the TV setting on Canon) at one stop above the longest setting on the lens. That's a great lesson I learned eons ago in the Nikon school of photography. For an 18-400 lens that would 500th of a second. I also set the ISO to 800 (or 1600 on cloudy days) giving me a good range for depth of field. I also shoot JPEG + RAW which gives me the post production capability of correcting many of the unexpected errors that might occur. AND I took many many photos which gave me the choice in what I wanted to keep. Enjoy your trip. Remember this rule of thumb: You can always delete duplicates or triplicates but you will always kick yourself for NOT taking the photos you wish you had.

I just returned from two weeks in Africa three days ago... I don’t think you need to worry about going back and forth between birds and wild animals... I found myself in the moment with mainly the wild animals out in the bush. (Meaning, if you are shooting an occasional bird, they wee few and far between and did not affect my settings) What I found to be the bigger challenge was getting focus on the moving animals as they approached our land rovers. Any sort of back button focusing was too slow and constantly changing. I changed my settings back to shutter focusing when in constant/wide tracking and that worked better. I shot with a mirrorless Fuji that had tracking capabilities but nailing the focus on the eyes was challenging if they were moving, especially coming towards me. Shutter priority sometimes would work well but I tended to like more control over what was getting bumped up so I stayed in manual more often than not. I could dial in those settings pretty quickly and then we would stay with a scene for some time giving me plenty of time to fine tune settings... good luck and have a blast! Where are you going? I was in Kenya... the great migration has shockingly started in Tanzania. The guides were in disbelief. There has been a drought recently that they thought was causing it to start early.

Grace, each of us is different. I have never been to Africa but my retired ophthalmologist has been there 17 times already. He used two lenses, the 18-200 VR and the 500mm f4 that he rented. During his last trip he took his D750 with a rented 200-500 f5.6 and a 28-300 VR lens.
Some of his images (he is an amateur) have been published. I am sure your D7500 and the Tamron 100-400 should do an excellent job and the 18-300 will manage many subjects also.
I have nothing against using AUTO ISO but I prefer to be in control so I prefer to set the ISO speed manually and a good start is ISO 400. I seldom use Shutter Priority because I prefer Aperture Priority but I am careful enough to watch the shutter speed for the shooting conditions I am in so as to raise the ISO of the camera in case it is needed. Noise will only show its ugly face when shooting under dark conditions.
You should do well. Good luck to you and bring back some nice shots.