Yes, changing the pvid= settings in /interface bridge port will add matching dynamic untagged entries to /interface bridge vlan. Otherwise you have to remember to update both when changing the PVID on an interface. Note that by default Winbox only shows the ‘Current Tagged’ and ‘Current Untagged’ columns under Bridge > VLANs, it is worthwhile enabling the ‘Tagged’ and possibly ‘Untagged’ columns too as inactive interfaces do not appear in the ‘Current …’ entries.
If I define a “management” interface in /interface vlan, will it also be automatically added to > tagged > entries? (so, could I omit both untagged and tagged on this code line you mentioned?)
No, tagged membership of the ‘switch’ bridge role has to stated explicitly in /interface bridge vlan