The mid position valve will fire up the boiler when ever central heating is required by main house, the two port valve comes before the three port valve so if open water will circulate what ever position the three port valve is in, so if latched open the garage heating would also work all summer when just domestic hot water is called for, if, and this is the big if, the TRV heads have opened the TRV on any of the radiators. However one would hope in the summer the TRV's in garage will not be open, so no coolant will flow.
The other problem is should the garage TRV heads call for heat, unless using Hive heads the boiler will not fire up, likely again this will not matter anyway and likely the Hive wall thermostat will be activated for long enough for the garage to heat up anyway, but if it is considered that may not be the case, then using Hive heads then it will send a "demand for heat" to the Hive wall thermostat and so fire up the boiler.
In real terms there is no need for the rest position of the three port valve, the three port valve only needs the centre position and fully activated position as in centre position it will not heat any room unless a TRV is open. Because the valve also acts as a relay it is required, but main idea of the three port valve is to allow flow to the DHW using thermo syphon to cool boiler if power fails. With S-plan power cut can over heat some boilers.
I will agree plumbing is wrong, and also agree if
@98webp can get the plumber back and correct plumbing that is the best option, as to why a two port valve has been fitted I can only scratch my head and wonder, with today's electronic TRV heads no reason to have a separate valve for garage and house, it is like in the electric world having a 30 mA RCD feeding a 30 mA RCD, the motorised valve does same job as the TRV which with an electronic head is a motorised valve anyway, it is duplicating the controls.
If there were no TRV's fitted, then I am sure it could be wired to work as it stands. Normally 5 or 6 wires to a two port valve, depends if the N/C is wired or not on the micro switch, so:-
Two Port ------ Three Port ------ New Hive
Blue ----------- Blue ------------- Neutral
G/Yellow ------ G/Yellow -------- Earth
Brown -------- Not connected -- No 3 heating on
Grey ---------- Not connected -- Line supply also needs line supply from same supply as boiler.
Orange ------- Orange
White -------- Not used.
Also a link needed Line to number 1 common on hive.
The problem is domestic hot water may heat up when the garage central heating runs, and the house central heating is not running, so instead of the link Line to number 1 common if number one common is fed from white on three port valve, then garage heating will only work when house heating running and it would not heat the DHW supply unless required.
The proper way would be to convert to S Plan, but there are ways as listed to make it work, even if not perfect.