Retention offers

Depends on the manager.

1. Manager might bring it up sarcastically if the tasks which you were working gets delayed due to unavoidable reasons.
2. You might get more work and you cannot deny it. Leading to burnout or WLB issues.

Never, i repeat never every take retention offer from existing company. Remember the reason you started looking out in the first place. Also now your manager knows that you are looking opportunity and have flight risk, so might impact future projects and growth perspective.

If the retention offer was in their budget, why were they underpaying you in first place.
Ask them that, and then quit like a gangsta.

No, your life will be made hell.