Incorrect.
The Provisional I.R.A and Provisional Sinn Féin are one and the same thing. Indeed, intelligence reports from MI5, PSNI and Gardai all state that they are controlled by the Provisional Army Council. And, believe it or not, still have access to weapons. This security assessment still holds in 2023 and accepted by both sovereign Governments too.
PSF's armed wing, PIRA is more accurately described as dormant. Not dead, disappeared or left the stage.
PIRA, like PSF, is very much a left wing terrorist organisation. From their formation up to the early 1990s, PSF/PIRA absolutely refused to do any deals with either the British or Irish Governments.
What changed in the 1990s was Thatcher's deployment of the SAS in 1987 where PIRA came off worse each time plus Special Branch successfully foiling terrorist plots by both PIRA and the UDA weakened them hugely. Terrorists were more likely to be arrested, put on trial and imprisoned than they were to be shot dead. In short, Thatcher's whole of government and criminalising PIRA had realised its aims by the time Major took office.
In military terms, PIRA was defeated by the Security Forces and they could now be pushed towards politics in the form of PSF. This is exactly what the authorities had done to the Official IRA and the Workers Party by 1973. It just took longer to do the same to PSF/PIRA.
"We were saying the armed struggle’s failed, it can’t win. The jails are filling up, people are dying left, right and centre and the British are getting the better hand on us.
Obviously we knew in our hearts that we were deeply, deeply infiltrated at a very high level.
The armed struggle had to stop. We’d dump weapons, call the ceasefire, and then go into talks."
- Frankie Quinn, senior member of the PIRA's East Tyrone brigade, one of the deadliest of PIRAs cells.
I've quite a number of such admissions from multiple PIRA terrorists who admitted the same in 2003. You might be interested in Rogelio Alonso's book, IRA And Armed Struggle. Excellent book that deconstructs how PSF/PIRA worked, the myths they told to justify their murders and why they finally accepted the Belfast Agreement when they'd previously helped destroy Sunningdale of 1973 and the Anglo-Irish Agreement of 1985.
All terrorist organisations make deals at the point when they're facing defeat as Michael Collins' own IRA was or when they're militarily defeated as PSF/PIRA was (failed to take power with the Armalite on one hand and the ballot box in the other). Irrespective of whether they are right or left wing terrorist groups.
There is no peace process without the security forces and it is only possible once terrorists are so weak they cannot fight on or are defeated. The reason for that is terrorist organisations have a fundamentalist attitude