In that area around Haigeng Park, Haigeng Daba, and Dianchi Lu the temporary traffic restrictions do not apply to cyclists.

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.

@livinginchina, there are all those English teachers and other subject teachers already in China, who can easily have work permits renewed. There has been a trend over the last 10 years for more 'schools' to offer extra-curricular activities, mainly sports, which is attractive to both the parents of prospective students, and for some teachers. I am sure that 4 hours of paid sports coaching as part of any teaching contract would be attractive to many potential staff.

When I think of the French I learned in school, the phrase I remember most clearly is, 'écouter et répéter'.

It would be a good idea to carry your passports at the moment. I will explain why.
I went to the hospital this morning. Lots of additional controls outside and within the hospital. I could not use the Wechat health app to enter the hospital, as when I opened it I could not go forward without following the link the the foreigners declaration, however that button did not work. Luckily I had my passport with me, and I needed that to register manually at the gate.
Others may have similar problems.