Actually they all do, let’s look at recent aircraft programs outside of Russia and China.

1. Rafale– ACX general layout and requirements for technology demonstrator completed by 1982 (decision to proceed with development into combat aircraft 1984). Decision to proceed with Rafale prototypes 1987
M88- General design choices and concepts completed late 1970’s for future turbofan required, component tests 1978, HP fan bench tests started in 1983.Full development started in 1986.
Design and development of turbofan started before the aircraft.

2. Eurofighter– ACA (1982) replaced earlier ECA, becomes EFA 1984. EAP techology demostrator (1986), Contract signed for Eurofighter demonstrator 1988.
EJ200- development started in 1986
This one is tougher as requirements kept changing. However both Eurofighter and Eurojet both formed in 1986. Either way, development of the demonstration airframe and engine were concurrent.
https://apps.dtic.mil/dtic/tr/fullte…6.pdf#page=398

3. F-22– ATF (RFI 1981, RFP 1985-86) Lockheed/GD/Boeing team declared winner of DemVal 1991, contract for EMD
F119- JAFE contracts for demonstrator engines 1983, Contract for EMD 1991
Demonstrator contracts for engines signed after ATF RFI and before RFP.

4. F-35– JSF (1986) Contract demonstration phase (1987) Lockheed SDD contract 2001.
F135 & F136- F136 pre-system SDD phase 1996, CDR 1997-2003……. F135- JSF 119–PW-611 (1997), F135 CDR 2003
Again, engine development started concurrent with aircraft demonstration contract.

So, yes, the engine development generally starts at (or even before) the time requirements for the the aircraft are defined.

MFI
start of work – 1981
MiG 1.44 was built in 1988-1991
The first flight was planned in 1992
Serial production of MiG 1.42 in 1995 at the Sokol aircraft factory in Nizhny Novgorod.

S-22 / S-37 / Su-47
beginning of work – 1983.
full scale development – 1988
May 1989 program closure
construction of a prototype at the expense of own funds of the company 1992 – 1997

T-50 / Su-57
preliminary work 1999
the beginning of the work on the program “Fighter – 21” – April 2001
In 2002, the T-50 was chosen from two Sukhoi T-50 and MiG E-72 projects.
2003 – 2004 – protection of the draft design. Started flights on the “flying laboratory” Su-47 with a new weapon compartment
March 2007 – the beginning of the construction of the T-50
June 2009 built T-50KNS, T-50-0 and T-50-1
January 2010 – the first flight of the T-50

Btw why did they use D-30F-6’s to propel Su-47? Since much of the airframe was based on Su-27, why not use AL-31F?

The AL-31F is not powerful enough for a heavy Su-47 fighter. The R179-300 engine with afterburner 17,500 kgf was not ready at that time. AL-41F (ed.20) did not give the firm Sukhoi

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https://www.defensenews.com/opinion/commentary/2019/05/03/russian-defense-spending-is-much-larger-and-more-sustainable-than-it-seems/

Firm “Antonov” not lucky with the country.

Presumably, the engine of the “first stage” provides cruising speed M=1.3. The engine of the “second stage” of not less than M=1.78

Production of the MiG-23B / BN established in Moscow, the plant “Banner of Labor” (“Знамя Труда”)

Tasks that performed f-4 Phantom in the US air force in the USSR air force performed three types:
Su-15, MiG-23 and Su-24

F-104 in competition with the MiG-21
F-106 compare with su-9 / su-11
F-101 – Yak-28P and Tu-128
Su-15 it makes sense to compare with the F-4
I Think it would be fair