The peeing into a funnel with a scale below is called a Uroflow test. The instrument logs the flow rate and total void volume. It's a quick, non invasive test used to screen males for prostate and other issues. The graph shows the flow rate vs time and if you start and stop.
If you are "Bladder Shy" the results may not be valid.
The more comprehensive test is called Urodynamics. In this exam small cath (Fr 😎 is inserted into your urethra and a similar cath into your rectum. EMG electroges are applied between your anus and urethra. You are fully exposed in the "frog" position.
The catheters measure internal pressures and one is used to slowly fill your bladder with saline. The pressure vs volume is logged and you are asked about feeling need to pee etc. You are filled until you leak pee. When you are filled, you pee into a Uroflow meter. They may x-ray you as the test proceeds.
The test takes about an hour and is embarrassing beyond belief.
Simple urine samples are usually taken "mid flow". The person is supposed to start peeing on the toilet and part fill the sample cup from the continuing flow. Sometimes, I think people are cathed to get a sterile pee sample.
Bladder filling for play is a REALLY, REALLY bad idea. Complete sterility is an absolute must.
UTIs can get you into big problems.