Is this buy rating for short term or long term buying on Groww?

Don't trust these random aggregated stats that you can't even verify. You don't know when the buy rating was given.

More over, there's a significant lag between the analysts releasing their signals in public vs releasing it to their paid customers.

Also pump and dump exists. In other words use it as a belief that the stock is generally accepted to have been bullish but also accompany with other factors on if it's hitting it's resistance, buying and selling volumes and bit of other TA.

I am surprised that people rely on such data for making an investment decision.

Generally long term but, after each quarterly results the ratings are updated. Since ratings depend on financials and outlook.

Depends on the analyst but usually means a mid-long term