Shall I apply for an M visa with a PU letter or for a renewal of my Residence Permit ?

Dear Sir or Madam,

My wife works as a teacher for a British School in China . We both have had residence permits for many years which are renewed annually provided her contract of employment is renewed.

She is now in China I am in the UK. My residence permit expired in July 2020. Her employer arranged a PU letter which was sent to me in early September and I was told to go to the embassy in England to apply for a visa (M) then they suggested once in China I could apply to renew my Residence Permit.

More recently at the end of September the Chinese Government said that for those with expired Resident Permits they could go to the Chinese embassy in their countries and ask to renew the Residence Permit. The communication said to take your passport, show the expired Residence Permit and provide the supporting documentation to the embassy and they will renew the Residence Permit.

Can you please help me to clarify the following:

Which of the two types of request shall I make: i.e. Shall I apply for a M visa with my PU letter or Shall I apply for the renewal of my Residence Permit (if this is the case – what supporting documentation do they refer to?).

Does it matter which approach I take?. Is one approach easier or cheaper than the other?

Please note I asked this question by email to the company that they say we should approach for visas but they do not respond. I have navigated their websites but they are not clear and the format and information on the website is very difficult to understand.

Thank you for any comments and advise you may provide.

Billy.