I bought the app on Huawei AppGallery, but now I have a phone from a different brand. Will the purchased license from AppGallery apply to the app from Google Play?

No, because the app's license is provided by the store where the app was purchased. However, in this situation, the solution would be to install AppGallery on your new smartphone (regardless of its brand) and use it to install your purchased version of the app.