The body has several well-regulated mechanisms for handling it.

If semen isn't ejaculated, the body reabsorbs the sperm in the epididymis and recycles the cellular material. Seminal fluids, which are produced during arousal, are either reabsorbed or, in cases like retrograde ejaculation (e.g., with alpha-blockers), pass into the bladder and are later urinated out. The system self-regulates; there's no harmful buildup to worry about. :)

So, TL;DR: You will just urinate it out in our case.

I wonder if this leads to higher risk of prostate cancer, as an inverse to studies on relatively frequent ejaculation lowering prostate cancer risk.

From what I gathered, it does not appear to have an impact on prostate cancer risk since the prostate still undergoes stimulation and fluid production, and the contents are still expelled.

Silodosine-induced retrograde ejaculation does not prevent ejaculation from occurring, it simply redirects the pathway (different anatomical exit).

It is different from chronic ejaculatory abstinence.

What do you think happens with a vasectomy? It gets reabsorbed.

With a vasectomy, you still ejaculate. Most of the fluid in an ejaculation comes from the prostate, which isn't affected by severing the vas deferens

Hmm, I wonder if it's really unaffected. Have they found a mechanism for the small but statistically significant increase in prostate cancer rates related to vasectomy?

Vasectomies don't prevent ejaculation. The semen is just sperm-free (after a brief period of time).