I’m a retired US physician. Yes, to answer the OP, but only once as his patient from another physician, in a urologist‘s office about 47 years ago right after college. I had symptoms of prostatitis including poor emptying and post-void leakage, so he was doing a true clinical diagnostic massage, or”milking,” to push some prostate fluid out my penis tip onto a slide to look for infection. The vast majority of standard transrectal (finger through anus) clinical prostate exams, also abbreviated DREs (Digital Rectal Exam) are done with 3 main goals. First is to feel for the presence of either anal or rectal masses (possible tumor or abscess), second is to test the withdrawn finger for rectal blood (wipe finger on a card, see color change) to screen for colorectal cancer, and in men, third to feel the size and consistency of your prostate (enlarged or irregular “bumpy” feeling gland may indicate tumor or other enlargement). You definitely feel the finger going in and feeling around to feel your tissues, but very little pressure.
OTOH, if the doc needs to obtain prostate fluid to look for bacteria or other species, it requires much more pressure directly on your prostate to “squash” or deform the gland enough to push prostate fluid all the way from your gland out the tip of your penis. It feels very noticeably different from a DRE because there’s much more pressure on your prostate (front or anterior wall of your rectum) usually for a longer time, until enough fluid comes out your tip. When mine was done, I felt a great deal of pressure moving all around my gland which was almost painful, but not quite. He pushed enough fluid out onto a glass microscope slide and then withdrew. In my case, he did find bacteria producing my symptoms of prostatitis and treated me successfully with an oral penicillin analogue.
When you massage or milk yourself or your partner for enjoyment, many men including me will feel fluid moving from the very deep part of your penis all the way up the urethra until it drips out. To me it’s a pleasant sensation of fluid movement a lot like urination in addition to the actual prostate pressure from the finger or toy. Some men may not feel or see the prostate fluid depending on the amount of pressure and length of massage. With longer, firmer massage, you may also feel stronger periodic brief contractions of your gland and/or spurts of fluid ejaculating, which many would call a “prostate orgasm.” For myself at 69.5+ now with serious ED from medication, I do it relatively frequently with a SS toy called a PureWand as a pleasant erotic substitute for normal masturbation because just pushing and massaging my prostate feels a great deal like a semi-continuous orgasm as long as I care to massage it.
Eric