VS use Terminal 3, not 4.

They have a nice arrivals lounge, which is landside so you’d need to clear immigration, collect your luggage, walk through customs and go upstairs to the lounge with your luggage (which they’ll store while you’re in there).

The main advantages to going to the VS arrivals lounge as opposed to straight to T5 would be to use their showers which are 1,000% nicer than BA’s dreadful facilities, and to enjoy a full breakfast which is also nicer than the offering in BA’s lounges.

You’d then need to walk to Heathrow Central rail station (5-10 minutes via a pedestrian tunnel), catch the Heathrow Express or Elizabeth line train to T5 (6 trains an hour, free but you do need to get a ticket from the machine to operate the barriers) and check in again with BA at T5 where you’d then have access to their Club lounges.

You’d need to leave the VS arrivals lounge about 2 hours before your BA flight departs to be safe, so YMMV on whether you’ve enough time to visit, or just go straight to T5.