For a Stational Mass of the Diocesan Bishop the instructions are for all to sit when the bishop sits. From the 1984 Ceremonial of Bishops:
“166 When the bishop returns to the chair after the communion, he puts on the skullcap and, if need be, washes his hands.
All are seated and a period of prayerful silence may follow, or a song of praise or a psalm may be sung.”
(Ceremonial of Bishops, Liturgical Press, 1989, ISBN 0-8146-1818-9, page 60).
This should still be followed, since from the 2002 General Introduction to the Roman Missal (GIRM) which can be accessed from
romanrite.com/girm.html it has:
“112. … At a Mass celebrated by the Bishop or at which he presides without celebrating the Eucharist, the norms found in the
Caeremoniale Episcoporum should be observed.”
The “Caeremoniale Episcoporum” is the Latin title of the book “Ceremonial of Bishops”.
For other Masses the 2002 GIRM will apply. Here the instructions on posture after Communion are not clear.
On the one hand unity of posture is encouraged. For example: “42. … A common posture, to be observed by all participants, is a sign of the unity of the members of the Christian community gathered for the Sacred Liturgy: it both expresses and fosters the intention and spiritual attitude of the participants.”
Another example of unity of posture is: “43. … With a view to a uniformity in gestures and postures during one and the same celebration, the faithful should follow the directions which the deacon, lay minister, or priest gives according to whatever is indicated in the Missal.”
On the other hand “individual freedom of choice” seems to be encouraged by this part of 2002 GIRM n. 43: “… and, as circumstances allow, they may sit or kneel while the period of sacred silence after Communion is observed.”