Even the best run and organised reception classes are busy, noisy, crowded places. For a child who has been used to being at home, largely 1-2-1 with adults, in a quiet environment where every request, observation and comment is immediately noticed and responded to then getting used to the maelstrom of a free flow classroom takes time.
Your daughter has to negotiate many new relationships, with adults, with peers. Many new places, Classrooms, hallways, outside play areas, lunch rooms, toilets. Many new expectations, sitting quietly, sharing, tidying up. It is not surprising that she is taking a while to take it all in, especially as you say she is quite shy to start with and has had periods of illness.
To be honest the school sounds good, (STEM week yeah!!) , they are noticing her, observing what she likes doing, trying to encourage her to extend her range of activities, praising her for success , noting improved communication with others. They sound on the ball. Keep up the dialogue with her teachers so if there are concerns on either side you are both aware of them, but by and large keep doing what you are bothe doing.
I wouldn't start new activities at this time of year, the last half term of this term is a hard slog for everyone, and for a tired reception child even harder. Keep on with the swimming, get out in the fresh air at weekends, have good down times at home during the week.
She will make friends, but the friends she makes are probably in the same situation at the moment, a bit overwhelmed and a bit tired. Children's friendships are not set in stone, they are flexible, just because you don't have a best buddy at four doesn't mean you won't have one at five.