TRACON Controller reported an aircraft on approach was transferred to tower then responded to a TCAS/RA for VFR aircraft in its path resulting in a NMAC.

Narrative

Aircraft X was vectored onto the localizer for the ILS 3 at ATW due to low visibility from smoke. After clearing Aircraft X I noticed two aircraft in ATW's airspace transitioning southbound that appeared to be a factor so I coordinated with ATW to verify they were in contact with the two VFR aircraft. ATW confirmed they were talking to the two aircraft and confirmed they were transitioning southbound. I then transferred communications for Aircraft X over to ATW so they could issue traffic and develop a plan to avoid the conflict. ATW tower allowed the two VFR to fly through the glideslope at the final approach fix instead of controlling the situation to avoid the conflict. Aircraft X descended on the glideslope to the same altitude the two VFR aircraft were at resulting in an RA. Aircraft X followed the RA instructions and then ATW transferred back to me for the ILS 3 again which they completed uneventfully. I noticed the conflict when the aircraft were still several miles apart and made sure to coordinate with tower to ensure they were in contact with the two VFR's so that ATW could prevent any conflict. The ATW controller apparently issued traffic but did nothing to prevent the NMAC. The situation is a very common one with arrivals to ATW and we always call to verify that ATW is talking to the VFR aircraft before transferring communications to avoid unsafe situations. The ATW controller did not make any action to prevent a mid-air collision and as a consequence the NMAC occurred and was averted due to the TCAS RA from Aircraft X. ATW should have had the aircraft remain west of the localizer for Aircraft X until he was past them on the localizer. Under no circumstances should he have allowed two aircraft to be along the glideslope while another aircraft was conducting the approach. The ATW controller's actions were downright dangerous bordering negligent in allowing the two VFR to fly right through the approach with a business jet on the ILS.