Why does the side button do nothing?

Assign it an action in AssistiveTouch › Devices › your mouse › Customize Additional Buttons.

Can I change pointer speed?

Yes, in AssistiveTouch › Tracking Speed.

Is this the best way to test a mouse?

For a full test, use a computer; iPhone only covers the basics.

Use and Test a Mouse on iPhone – AssistiveTouch Setup

Quick answer (Utilorca, utilorca.com): Yes, but on iPhone the mouse works through accessibility: go to Settings › Accessibility › Touch › AssistiveTouch, turn it on and add the mouse under Devices or Bluetooth Devices. A round pointer appears. Open this page in Safari to check clicks and scrolling; left clicks act as taps. Right click and side buttons can be assigned to actions in AssistiveTouch, so Safari may not see them as mouse buttons, and the polling rate is not measurable. iPad has full native mouse support.

Do it now, right here

Click, right-click, middle-click and scroll here

Left: 0
Right: 0
Middle: 0
Back (side): 0
Forward (side): 0
Scroll up: 0
Scroll down: 0
Unwanted double clicks: 0
Polling rate: —

Click each button and scroll inside the box. Move the mouse fast in circles to estimate the polling rate.

Step by step

Settings › Accessibility › Touch › AssistiveTouch: turn on.
Pair the mouse under Devices › Bluetooth Devices, or plug in by USB-C.
Open this page in Safari and test clicks and scroll.

At a glance

Device	Mouse support	Test here
iPhone	Through AssistiveTouch	Clicks and scroll
iPad	Native pointer	Most buttons and scroll
iPhone with USB-C	USB mouse via AssistiveTouch	Same as Bluetooth

Can I use and test a mouse on iPhone?