There is a sea change in Pakistan Iran relation since Israel attacked Iran a few months ago where Pakistan came out strongly condemning Israel while India didn't even publicly named Israel. Iranians have not forgotten that. Even Trump, after the 'private lunch' with General Asim Munir said that Mr. Munir was 'not happy' about the attack on Iran and Pakistanis 'know Iran more than most'. So there was Pakistan advocating for Iran and perhaps the sham tit-for-tat of Iran-America attacks were agreed upon in that lunch.
So there is a good chance Iran will help Pakistan in some way in case of a conflict against India.
But capturing Karachi city??!! India may try to capture the Sir Creek / Rann of Kutch and that's about it. They will sing songs for that for the next 60 years like they still do for the 1971 War.
If India did end up capturing Sir Creek/Rann then its worth singing about...
However, realistically, I don't think India wants to "invade" Pakistan esp. as the end-game is not in Indias favor. I don't believe strategic planners in India will not understand that India doesn't gain anything by occupying Sir Creek or for that matter even Karachi
After all, all wars end on table (incl. where the other side has clear victory). And India knows that on table it will be hard to occupy territory beyond IB. Professional army learn lessons from victory and defeat and don't "plan" something just to prove a point or revenge. I believe Indian Armed Forces are one of the most professional ones out there, never crossing lines without consensus across the board
If members here believe Modi wants to invade to stoke passions, they are wrong (IMO). He has won three terms without on-ground invasion (across IB and Uri was localized action) and he has many fissure points he (more like his subordinates) can use to segregate.
Many people see Modi has an egotistical demon but any politician who's garnered respect, accolades and by and large enjoyed good relations with his counterparts over almost 12 years can't be uni-dimensional. By extension, nor is India's policy or perspective of every situation. Also, geopolitical reshaping is a constant exercise - sometime in your favor and sometime not. I don't think India has "lost" the improvements in ties with US and larger western world which started post 9/11. Sure Russian situation is tricky but India has recently signed pretty good deals with UK, other European nations.
All in all India doesn't gain anything from attacking Pakistan but the red lines are also clear (whether the world wants to agree or not). I don't see Modi/Indian gov going back on these if there is another Pahalgam style attack. Its kinda bad as India is now in a corner as their hand is forced but its the price you pay...