No need for official restriction but they can do "unofficial" like this one. Just expose their statements using media or NGO then use some proxies to elevate the issue and you are done.No need to do anything to H&M. Fast fashion like H&M and Zara are on the decline with China's youths as they pick longer lasting apparel. In addition the European styles of these two retailers do not gel with Chinese street fashion - Balenciaga, SheIn, Uniqlo are much more popular with Chinese. Just let these fast fashion die a slow death as it is happening.
No one cares about Fila and New Balance. Nike is the bigger concern. Maybe just air on social media what Nike is doing to Chinese youths and they should switch to Adidas, Anta, LiNing. But Nike is still really popular which sucks - maybe at this point the Chinese government should create an app compiling the companies that insulted China such as Dolce & Gabbana, H&M etc and let Chinese consumers vote with their wallets. They can just consult the app on which brands to avoid. No need to officially restrict fashion brands as this makes the Chinese government look petty.
Maybe not a full assault against Nike as they are a huge Corp but definetely a strong one so that Nike and the other companies learn their lesson and start sourcing from Xinjiang which will help the local economy there