Is 2 hours 50 mins sufficient in Heathrow to connecting flight with different tickets and airlines

I made it to Finland through LHR from India on 27th June. Below are few points experienced in my whole journey:

1. At start point in India, AirIndia airlines checkin staff was not sure if I can travel to Finland via LHR holding a resident visa of Fin. They literally took more than an hour to understand if its possible, by checking gov.uk website.
2. After they convinced that transit is allowed in LHR, I made a request to pass through baggage all the way to Helsinki though the connecting flight was on another ticket and not partner airlines. The officials was ready to do that but I had a excess bike box baggage due to which they denied and suggested me to reclaim the baggage in LHR and proceed with recheckin.
3. On my arrival in LHR, AirIndia flight arrived in T3 rather T2 where I have Finnair connecting flight.
4. Flight exit priority was given to business class followed by transit passengers, I quickly got out and reached UK border control check point.
5. Was in a doubt with next step, went to security staff and explained him I have a connecting flight in T2 but I have to reclaim my baggage. Time now was 7:30 AM 28th June.
6. The staff was really helpful, he called up relevant folks to understand if I can transit from T3 to T2. At this point I was quick connecting to LHR wifi, opened gov.uk transiting info pages, did made him understand I am following rules mentioned in website about same day landside transit, TWOV etc.,
7. However, staff mentioned that considering the current Covid situation ground rules are different to what’s updated in website. I was in little dilemma at the moment. Staff asked me to wait further until he gets approval for me to transit.
8. Around 10:30AM, staff person came to me raising a concern that Finnair is not allowing red list passengers and I might end up in quarantine in LHR. I replied him the current Finnish border entry restrictions wasn’t applicable for resident’s but again he confirmed ground realities are totally different.
9. At around 11:15AM, after Finnair gave me approvals to board, staff escorted me to immigration officer at border check, allowed me to explain my itinerary. The officer immediately provided an exemption to reclaim my baggage and reach T2 by providing managed quarantine slip (MQS) for one day as shown below.

10. Reached T2 by 12:15PM, waiting till 3PM where check in begins, and I was the first to do that. Followed by security check, where I was asked to dump all perfume bottles etc., which are beyond 100ml. Finally I am in to gates and boarded flight at 18:10PM and reached Helsinki by 21:30PM.

To conclude, never ever book two different tickets for the journey until no other options available. If yes, keep a good amount of duration between the flights. Also until Covid situation exists everything is unknown.

Would like to know if ~2.5 hrs is sufficient for entire recheck-in/immigration/customs process?

I would give it a 50/50 chance at best.

Heathrow immigration wait times can be substantial: you can check recent performance here https://www.heathrow.com/company/about-heathrow/performance/airport-operations/border-force-performance-reports

It’s also a bit of a rush hour: a lot of the US and middle eastern flights come in between 7:00 and 8:30. Covid controls or confusion often slows things down as well.

On the plus side, your flight is unlikely to be full and if things go "normal" you will actually arrive earlier since the airlines often pad the schedule to improve their apparent online performance and avoid delay compensation.

Any possibility where I can save time in the process?

1. Don’t check luggage, use carry on only
2. Use an EEA passport if you have one https://www.heathrow.com/arrivals/immigration-and-passports
3. Any type of status with airline and/or a higher class will help
4. Try to get a seat at the front of the plane to Heathrow. You can also alert the flight attendants that you have a tight connection. If you are lucky they will get you out first or early.
5. Make sure that you are fully familiar with the most recent Covid requirements and that you have all required documents printed on paper and ready to pull out quickly.
6. Download the Finnair app and see if you can check in online. You may be able to do this while you are still in India, but due to Covid online check-in for international flights is rare and chances are you need to go to a counter for a doc check before you can get an actual boarding pass.
7. Make sure you meet all legal Covid requirements. Since you are on two tickets, you are may NOT be covered by a transit exemption and may have to meet all requirements for entry from India into the UK.

If everything runs well you might make it, if only one thing takes more time than planned you will miss your second plane.

It usually takes between 30 and 90 minutes from the plane seat to outside the luggage collection area. Most airlines ask you to drop your luggage at least an hour before the flight but longer time spans are possible. And if you drop your luggage at the last moment you will have to be very quick through the airport as you will have no spare time.

You see you do not have a lot of time if things are a bit slow, no time at all if your route through the airport to your luggage (or luggage delivery) takes a lot of time.
And that is assuming it is in the same terminal. If you also have to move between terminals, forget it. No way possible at all.

Usually people advice 4 hours or more between flights if on separate tickets. But with a long flight as the first of the set, I would want more time.
It might be needed to buy a second ticket to Helsinki, or at least move your flight by 4 or more hours, 24 is more likely.