(One quick note for those who don't want to wade through the rest
Setting exposure compensation, or adjusting manual exposure, for high-contrast scenes requires practice. Per the below, the OP would not have had to make an adjustment in this case, but against a darker background, it would certainly be appropriate. There's no substitute for experience, bracketing, and analyzing results.)
How about supplying your camera and exposure information so we do not have to look it up? ....
For exif viewing, this site is quick and easy and doesn't require your passing the "I am not a robot" test, which I invariably fail
f/8, 1/1250 sec, ISO 200, 480 mm on 200-500 mm lens, aperture priority with -1 EC.
I don't know if it's possible, without information from the OP, to know how much the polarizer affected exposure; however, in checking the histogram in PS Elements ACR, I could easily take the image 2 stops lighter without losing detail in the swan. The question is where to gain the two stops without lowering shutter speed or changing aperture. In this case change ISO to 100 and set EC back to zero.
This flexibility with exposure is important to know, because when shooting wildlife you have to prioritize and you often have to make decisions quickly if you're going to capture the moment.
IMO the most important is a fast enough shutter speed to prevent motion blur. #2 is aperture for the depth of field you desire. Using this calculator
will help decide appropriate aperture: the further away you are, the more dof you can enjoy at a given f/stop.
Steve Perry's name came up in the thread posted to Analysis. His website ishttps://backcountrygallery.com/
And his UHH user account ishttps://www.uglyhedgehog.com/user-profile?usernum=60547
He has topics and links posted to UHH + many e-books on his website for those wishing to explore further, including when to use auto ISO and when to use burst mode. He is a great resource for this forum!