Need guidance on H1B visa transfer case

I have a stamped H1B visa valid till Oct 2023. Currently, I am in India and have never travelled to US before. I got the stamping through my previous employer X. The stamping happened in 2020. But since it was COVID period so I couldn’t travel to US and the end client reverted the offer. Hence, in 2022 I thought of transferring my petition to some other company and try to get an employment in US. Initially, I approached a company Y. They helped me transfer the H1B petition and became my sponsor. But they couldn’t send me to US as they didn’t have proper clients at that time. So, this forced me to approach one more company named Z who promised to help me get a job in US. The company told that I have to serve in India for 6 months and then only they can take care of transfer. Based on their commitment I joined them in India and they transferred the petition. But they even could not send me to US citing there is recession going on in US. Hence, I resigned and joined somewhere else as I was underpaid in company Z wrt job market trends in India.

In a nutshell, I am currently not employed with any of these 3 companies but I have 3 approved I-797 petitions out of which one is going to expire in 2023 and other two are valid till 2025.

So below are my concerns:

  1. If I can’t travel to US before my Visa expires(which is going to expire in this October) then what are the chances that I can travel to US with the other existing petitions?
  2. Will I still be considered under H1B cap exempt, even if I have never travelled to US and my H1B visa expires?
  3. Can I approach any other company again to file my petition without going for H1B lottery process after visa expiry?
  4. Is there anything else I can try to get a job in US after visa expiry?​

Inputs are appreciated.

I-797 is not a visa and you can’t travel on I-797. You need H1B visa stamping. Also I-797 is employer specific so you can’t use it for another employer. Whoever hires you will file a cap-exempt H1B petition for you and once approved you will need to apply for H1B visa at the US consulate in India.
You can only travel to the US if the H1B sponsoring employer have a bonafide H1B job for you.