Assuming that there is no minimum volume for a stable transition, and engineering is a one tonne minimum.
Automated would remove the need for a bridge.
So, maybe five tonnes.
As I recall, my manned design was twenty five tonnes as the smallest viable starship.
But current canon is hundred tonne volume minimum, and ten tonne jump drive default minimum.
HG2 lets you comply with all starship requirements except the 100Td minimum in 30Td.
TL9, J1/1G/Pn1 (1Td each), 20Td bridge, Mod/1 comp, 1/2 stateroom, 4Td fuel.
MCr12.165 as flattened sphere, w/o class discount.
Minimum drive size is 1Td but fractional sizes above 1Td are allowed (HG2, p. 34).
- in 30Td, 1Td jump drive (3.33...%) could be J-2 (only J1 in this case).
- in 30Td, 1Td maneuver drive can only do 1G.
- in 30Td, 1Td TL9 power plant is Pn-1 (1.11...)
Minimum power plant fuel is 1Td (HG2, p. 34).
Minimum starship bridge size is 20Td (CT,
passim). Cost is by
ship tonnage (HG2, p. 27).
Jump fuel is 10%*Td*Jn; 3Td (
ibid).
2Td Half-stateroom allowed by TCS (p. 15), while only implied in LBB2 and LBB5.
J2/1G is probably possible in 35Td, but the Jump Drive and power plant will need to be enlarged by a fraction of a ton each, in addition to the additional jump fuel requirement and upgrading to a Mod/1bis.