This is likely similar to how we currently treat missiles under DR. While we would consider dedicated missile launchers toward the DR of a ship as the maximum Tier of missile they could fire, ships are often allowed to have a small number of belly-mounted or wing-mounted missiles (up to four in practice that I've seen, but never really defined to my knowledge) that aren't counted. As such, it would likely depend on how many mines you were carrying in this instance since your craft isn't employing minelaying equipment. For reasons listed below, STL Mines could double as missiles, so they'd have to count as active ship weapons.
STL Mines would have to move as swift as a missile to have a chance of working, if only because of how absolutely massive space is and the low density of mines in a given area. That space would also likely have to be limited to being within a star system or key areas of it. The necessary number of mines for even covering that "limited" an area would be more massive than any single ship could ever hope to deploy. It's probably one of the reasons mines have seen a decline in use. STL minefields take time to put up even in that limited a scenario and the sheer number of them means you're better off using those resources to make more ships once covering a large enough area.
FTL mines are far more interesting, and something I want to make/implement as well. Current weapon rules only allow for ramming attacks and nothing else employing FTL (even FTL-capable missiles have to drop to STL before delivering explosive payload), so the FTL mines would have to convey most of their damage via ramming and perhaps the effects of destabilizing the enemy ship's propulsion. If a ship is hit by an FTL mine, nearby FTL mines can then capitalize on the advantage if the ship is knocked to sublight speeds and cannot recover, even if it managed to survive the initial strike somehow. FTL mines would also have to be evadable to a degree due to the large distances involved and to be at least potentially survivable for the defenders without explicit point defense options. Some newer Yamataian ships like the Plumeria 2E, Chiaki 1B, and Azusa have countermeasures for FTL ramming attempts that make it easier for them to evade, but other craft likely do not.
TL;DR, we need to define balance.
Given that FTL mines will likely not have the same speeds as ships, their placement will also be important to plan and they will have to act like the STL missiles you describe. Their speed will act as a force multiplier of sorts that allows them to be deployed in densities that are somewhat attainable to cover an area, but not foolproof. They likely also have the capacity to act as STL Mines/Missiles and likely count as active ship weapons because of that.