I'd suggest starting from Volume 25 of the manga. It aligns well with where season 5 ends and takes the story forward smoothly. There might be a few differences in pacing compared to the anime, but it'll give you a seamless continuation.
After season 6 of MHA, a good place to start the manga is around chapter 315. This chapter continues the story arc and keeps you engaged without feeling lost.
Another fictional hawk could be 'Hawkeye' which is a name that can be associated with a hawk - like character. It gives the impression of a character with sharp vision and a focused, predatory nature, much like a real hawk.
One option is to check out official manga subscription services. Sometimes they have the continuation of MHA after season 6. Another possibility is to look for dedicated MHA fan forums or communities where members might share links or information on where to read it.
The Hawks' back story could involve their origin as a sports team. They might have started in a particular city with a group of passionate players and investors. Maybe they were initially part of a smaller league and then grew to be in a major one. Their name could be inspired by the characteristics associated with hawks, like speed and precision.