If I resign my job I got as Skilled Worker Visa, Can I stay in UK for some days?

I am a US Citizen, got Skilled worker Visa and came on December 10th 2021 to UK , started job 4th january.
If I resign from the job now(as it is not what I had expected),
1) Can I stay for a couple of months to travel around UK before leaving the country?
2) If not, can I just go to some other country(Say Paris, France) and then come back on my normal US Citizen passport(no need for a visa to enter UK) and enter UK for a couple of months?

Put in a different way, I want to finally leave UK back to USA June 30th. How do I calculate back to the date I should resign? (including a 60 day period after resigning and informing the Home Office, and getting back a letter from them, as seems to be the process).
thanks,
Badari

When you resign, or at the end of the notice period if you have to give notice, your employer will inform the HO that they are no longer sponsoring you. You don't have to contact the HO. The HO will then curtail your skilled worker permission to 60 days. The 60 days are counted from the date of the curtailment letter you'll receive, not from the date you stopped working. There can be quite a lengthy delay in the HO issuing the curtailment letter but it is not possible to predict how long, this will depends on their workload.

During the curtailment period you can remain in the UK but if you leave the UK your status will end.

If you return to the UK either before or after the end of the curtailment period, and as you are a non-visa national, there is no reason why you shouldn't be able to enter as a visitor but if your details are checked at the UK border be prepared for some questioning.

Thank you so much. This is really helpful.

Hi Manci
Reason I posted this question is a post I saw on some Manchester Immigration lawyer website: That sounded like eventhough I could stay 60 days, it is better to leave ASAP.
Any view on that?
thanks,
Badari

IF YOU RESIGN:
You may not be required to leave for 60 days, but it is advisable that you begin making plans to leave as soon as you are able to. This ensures you will not look like you aren’t complying with immigration law, which could affect future visa applications.