@Pete B. Looking at what @fabey posted. It would probably help to have on hand a copy of any documentation to show that you will be resident.
If it is for a job, get your employer to scan and email a letter to this effect, with an address where you will live (if that has been organized).
If for family reunion, get the family to scan email you a copy of the household ID, rental agreement, of the address where you will live. As well as a signed letter saying you will be living there, and a scan copy of the ID card of the person signing the letter.
You may not need these, and I am not saying that this will do the job, but it will go a long way to help baffling the bureaucrats into submission if they do start dithering.
In the past, I have heard of people being denied renewal if they left it to the last week. Since then I have usually applied 3 weeks before expiry, and it has usually taken two weeks to get the new visa.
At the moment things are quiet and processing time may well be a bit shorter, but I wouldn't risk it if I didn't have to. If I remember correctly the new visa was dated for one calendar year beyond the expiry date of the old visa, I didn't lose the weeks worth of cover. However, this was for a renewal at the appointed time, not an early renewal, as in the case in the above post. The last time I applied was May 2021.
As additional information to @livinginchina's list.
Ref. item 2. If you wife does not have a Kunming Hukou she will also need to bring her Kunming temporary ID and copies of that.
Ref. item 4. You need to get the passport photos from an authorized photo office, these produce a receipt with a bar code and your photo on the paper. This barcode is read by the PSB system. The photo office outside the Tuodong Lu building does this. The photo office for foreigners is in the outside wall, on the right hand side as you face the building, not the one on the corner of the building, it is about 10m further back.
Additional item. Your wife will need to write a letter of invitation, there is a standard form for this available in the visa office.
Things are still up in the air. However, I would speculate that teaching or tutoring school age children will be restricted, perhaps to the point of near impossibility.
However, teaching university students and adults is still permitted. Universities do not pay the best, but the contract is clear cut, there are usually no office hours (you teach 16 class hours max and the rest of the time is your own) accommodation is usually provided (sometimes an accommodation allowance) and flights home are paid. For those who have never worked in China before, universities are a good place to start and learn the ropes.
Adult learners are most common in the tier one cities like Shanghai, Beijing, Shenzhen, etc. When I lived in Shanghai I worked for 3 different companies over 3 years and I only taught adults.