In my case, it seems like the problem is caused by the Windows defender. Basically, it try to scan your computer during sleep. Because it's the intense task, fan is running. I disabled this in the task scheduler. I designate a specific time for this regular scanning (for example, Saturday afternoon at 2 PM). This solves the problem.
I've got a brand new Inspiron 16 Pro running Windows 11 Pro and have a #meToo moment about the fan continuing to run in sleep mode.  These seems to be a perennial problem.  Search the community fora for "sleep fan" and you'll find hundreds of similar complaints spanning many different Dell models over many years.  If I Hibernate my laptop, the fan stops as it should, so it's not a motherboard fault.  I've spent several hours browsing this forum and the net generally and this is what worked for me. The issue is that Microsoft have moved to a "Modern Standby" (S0 Low Power Idle) which still allows some software programs to run even in Sleep mode. The question is: how to turn that off and move to Standby S3 instead? This webpage gives the best explanation I found but below are my own experiences and idiosyncrasies: [URL] When I run the "powercfg /a" command described in that link, I got the exact output as shown, saying that Standby (S3) is disabled. I booted to my Bios and found in the Power section an option to Disable S3, however that was set to OFF. I.e. S3 was NOT disabled (S3 is enabled) which seemed a bit confusing given the powercfg output. I added the PlatformAoAcOverride = 0 Registry value as described and that didn't solve the problem UNTIL I remembered to reboot the laptop. Now sleep mode does what is says on the tin and rapidly sleeps the laptop with the fan OFF. Unlike the Modern Standby however, I now have to press the power button to turn the laptop back on, whereas previously just pressing a key would wake the laptop up, but this is exactly what I want. I hope this post helps you.  In true "1 step forward, 2 steps back" fashion, during this process I discovered 2 other problems I now have to try to fix (any help welcome!):1) "Hibernate" is not showing as an option in the Power menu2) The bios screen blanks the screen (turns the whole display off) for a second, every 3 seconds or so, which is VERY annoying!
Solution to Inspiron fan continues to run in Sleep Mode