score:4
Want to know what could be implications of missing entry stamp when I travel to India next time (somewhere towards early next year)?
None. You have the I-94 as proof
Does this impact my H1B Visa extension ?
No.
Also what can I do to correct this information on my passport?
Nothing required to correct. You can contact Customs and Border Patrol for Deferred Inspection if still uncomfortable and see if they will stamp your passport.
The I94 you have provides the same information, which is your entry date and status in which you entered. The stamp is NOT required. Back in the day they stamped the I-94 and attached to your passport. It was quick proof to anyone that you entered legally. They have all that information however USCIS is notoriously lazy so even when you apply for something else, they like you to provide the same evidence they have in their files.
You can get a copy of your I-94 here https://i94.cbp.dhs.gov/I94/#/home. The exit checks you encountered when leaving the USA is not the norm, the probability is probably less than 2% and if it happens you have your I-94 to prove you entered legally and in what status.