slow startup for imac

Assuming this is the 21.5-inch iMac running macOS 13.6 shown in your equipment line, please do "About this Mac..." from your Apple menu. Tell us what that shows for the SUB-MODEL (the bit with a year and sometimes with Early, Mid, or Late appended). Those are important to our remote diagnosing this

Also tell us what processor/chip type and speed that the "About" window shows:

However, your initial description ticks the "yes" box on two of the three questions I always ask to remotely diagnose a known issue with 21.5-inch iMacs made between 2012 and 2019: a slow and under-spec mechanical hard drive.

The third question is:

Once launched, do the apps seem to operate at normal expected speed?

Three "yes" answers says it's the hard drive. Fine when the computers were new, they tend to run poorly with newer macOS versions.

However there are crippled "educational/institutional" 21.5-inch iMacs with slow 2-core laptop processors that are even worse, thus my question about the "processor/chip" type. They also will not have "4K" in the sub-model name.

From there we can offer suggestions that will hopefully make what you have work better for you.

NOTE. Some think throwing more RAM at any "slow" issue is the universal fix. It is not in the iMac slow mech drive matter. If your hard drive is the culprit, no amount of added RAM will make a detectable difference in actual use.