Very good photo for 300mm and cropped. Post some photos with the subject filling more of the frame.
Also, having the attitude that the experience is way more important than the photograph is vital: Even if that photograph wins World Wildlife Photographer of the Year, the experience is still way more important, so enjoy it.
Most of wildlife photography is finding the right situation. If your subject is too far away, it will never look great regardless of the equipment one uses or the skill/experience of the photographer. To get a great image which shows good detail, most people are surprised at how close you actually have to be to a relatively small subject like a raptor, even with the best pro lenses.
But- and this may be true for you too-- it was quite heavy to carry on walks and hikes. And I'm 14 years younger than you. The 200-500 is heavier than the tamron 150-600mm. So think about how you'd use it and whether the weight is an issue.
Now that's a very nice photo. One thing I'd recommend is using a lower ISO, you'll get better details in your image (my most used ISO is 1000); 1000 is usually fine unless it's quite darker than it was when either of your photos was taken. I'm a bit older than you are, so you're not finished taking good photos nor are you finished learning and getting better.
Get down at the birds level

That's how you make the eye more visible... Remember you have a flippy screen and the D780 is a Z6 in DSLR clothing

so that is easy to do.
As someone who's longest lense is a manual focus 300mm, and an occosional 2x TC, I can say that there is bothing wrong with your photos that new gear would change. Heck, even the forst, heavy crop looks fine on screen! As pointed out, printing might be an issue, but then you can print quite large with only 7 MP, just don't look at it with a magnifier.
Other thaj that, nothing I could really ad that wasn't said already. I like how the Osprey seems to look at you in the first image. And the crane in the trees is simply beautifull.
Re:gear: one of the cheapest and easiest ways to get more reach is a DX-body, something like a used D500 or D7500 (if you some decent budget) or a used D7100/200. And a second body doesn't hurt anyway. Maybe even a used D300, I really liked mine for that!
@JDG Photo - yes, I will be doing that in the future, but cropping has its limits. I was thinking I could replace my D780 with a D850, and have 50 megapixels instead of 24. That simple switch would help me - a lot. If the camera is on a monopod, the weight won't be such an issue for me. Will do as you suggest - my next visit to Wakodahathee Wetlands should be fairly soon, before Florida becomes unbearably hot...
@Doomrider74: - Experience - yes!!! The more I do something, the better I (eventually) get. Need lots, LOTS more practice.
@Phil Seu: - I guess I need to force myself to NOT seriously try to capture those photos, or take them anyway for the practice, then delete later. On my next trip I will try to be more selective as to what I photograph. I usually "shoot first, and think later". I hope I will eventually accept what is beyond my limitations.
@AlanB313: I have (grudgingly) accepted what you wrote about the weight. Even on a monopod, I think that 200-500 is more than I can deal with. What are your thoughts on Nikon's much higher 40-400? So far, that looks like a reasonable choice for me.
@Woody Meristem: - I used to feel the way you do, but my Nikon D780 allows me to shoot at even 25,000 ISO, and as long as I'm processing the images in DxO PhotoLab, the noise/grain is mostly under control. Ken Rockwell posted a series of photos that shows how the detail decreases as the ISO reaches the stratosphere, but I'm no longer concerned with ISO - 2,000 or 5,000 ISO allows me to use a higher shutter speed, and perhaps a slightly smaller aperture, which I find very helpful. Thanks about the last comment - at some point age may be a bigger factor in my life, but maybe not for many years. I turned 80 this past December. Glad to read what you wrote!! Thanks!!!
@StefanSC: - I wil certainly keep that in mind for the future, but since I find myself on a "boardwalk" going around the wetlands, while I can't get as low as I want, maybe I can photograph birds further away from me, so I'm not "shooting down" at them. I will certainly keep this in mind for the future.
@hef19898: Yes, that Osprey is either looking at me, or my brother 20 feet to my right. I think you are correct though, since I was obviously following it, it makes sense that it was paying attention to me. This clearly shows in the photo. I posted the original photo to show how little of my image I used - and to improve in the future, a longer lens is an obvious choice, but switching from my D780 to either a D850 or Z8/9 would all get me twice my resolution.
I have no desire to change over to ML cameras, too old for this, and I'd likely be replacing most of my lenses too. The D850 might be the most obvious choice for me.
The D780 includes the "smarts" from the Z6, and I am just now trying to learn how to use them in ML mode (Live View) on my camera. I bought two books on the D780, and hope to learn how to do this. I don't think I will enjoy using the rear screen as much as using the viewfinder, but I want to try this for myself. Nikon did all this for a reason, but I haven't found a single person yet who understands this, and YouTube videos haven't yet been much help. I know I can use "tracking", but with animals I can't track "eyes" with my D780.
Oh and for my conclusion so far from this discussion, I now feel my picture IS good, but I want to do better "next time".
Thank you all!!!!
(How do I refer to other users, such that they know I replied to them? Is there a way I can type their user name here, that will let them know that I did so???)
(I have added the @ to the above user names - thank you!!!)