Since the end of 1943, three design bureaus (Mikoyan/Gurevich, Yakovlev, Lavochkin) were engaged in the development of a high-altitude fighter. But despite almost daily (!) government supervision, progress was extremely poor, primarily due to the lack of suitable engines. Yakovlev used the M-105PD (a modification of M-105P), M-106PV, and M-105PV (a modification of the M-105PF) engines with a two-stage SC of Dollezhal's design. The Yak-7 with the M-105PD, the Yak-9 with the M-105PD and M-106PV and the Yak-3 with the M-105PD and M-105PV engines were tested (designation in all cases was Yak-...PD). The main problem was engine overheating, requiring intermediate leveling off during service ceiling climb. In practice, the service ceiling of the Yak-9PD with M-105PD of early production was lower than that of the Spitfire VB (11100m vs. 11500m, for comparison: in the same conditions the P-39 reached 9000m, the Yak-1 9500m, and the MiG-3 10800m during the attempt to intercept a Ju 86R on August 22, 1943 over Moscow). The M-105PD was further modified by changing the SC gear ratios, but the problem of overheating remained. The M-106PV engine was equipped with an air cooling system after the SC using a water-alcohol mixture, the results were much better - the airplane could climb up to the service ceiling of 13500 m without intermediate leveling off. A speed of 620 kph was attained at the altitude of 10500 m. A total of 35 Yak-9PDs were built, 30 of them were equipped with the M-106PV engine.
The best performance was demonstrated by the Yak-3PD with the M-105PV engine: service ceiling 13300 m, 710 kph at 11000 m. Up to the altitude of 12500m the aircraft had good controllability and sufficient power to perform all the necessary combat maneuvers.
The armament was rather insufficient - one 23-mm gun, the aircraft was extremely lightened by reducing the fuel capacity, and the range was too short even for an interceptor. In spite of the fact that it was quite ready for serial production, theoretically able to fight both bombers and escorts, I have certain doubts about its real value. It was designed more for intercepting single high-altitude scouts than for attacking a formation of bombers.
Although the installation of an intercooler seemed to be an effective solution of the M-105 overheating problem even to that time, for some reason the Soviets did not make a try - it's a mystery to me. Nevertheless, the two-stage SC was brought to the required degree of reliability, production of both the M-106PV and M-105PV could well be quickly deployed (already in late 1945) if necessary.
Lavochkin tried to install a turbocharger on his fighters, but without much success - we can safely assume that the result was zero.
Mikoyan and Gurevich continued to improve the MiG-3 consistently - despite all the differences, their high-altitude fighters were structurally a further development of the MiG-3, while their engines were a development of the AM-35. According to some evidence Mikulin could afford a kind of "sabotage" - if he did not like the task, he invented various reasons for delaying the work. In the USSR such behavior could have dire consequences, but apparently Mikulin's merits with the AM-38 and AM-42 were valued so highly that the Soviet leadership forgave him his oddities. As a result, Mikoyan and Gurevich never got a fully operational high-altitude supercharged engine with desired performance from Mikulin. The solution was sought in the use of (initially) a low-altitude engine (AM-42B) with an AMTK-1 turbocharger, satisfactory functioning of which Mikulin did achieve. The performance of the I-225 was high enough to consider it a real threat to Allied bombers. Nevertheless, an engine with acceptable performance (AM-39FN2 aka AM-40) did not appear until the end of 1945, and its serial production began only in late 1946. It is difficult to say whether it was possible to accelerate its finalization, but most likely yes, a mass series could be expected in early 1946. In reality, from the middle of 1945 Mikoyan and Gurevich already focused on the development of the I-250 (another absolutely futile idea).
Thus, in early 1946, the Soviets could have fighters capable of intercepting the B-29 - I estimate the effectiveness as rather low, but B-29 losses could be much higher than in the raids on Japan if bombers were detected in time taking into account the potential numbers of Soviet fighters. The Soviets used radars, but the most industrial centers deep in the European part of the USSR had either completely inadequate radar detection or even not at all.
No new technology was required to manufacture these fighters, so they could be produced in fairly large quantities if necessary.
The most intriguing question is where the Soviets will get the high-octane gasoline for the manufactured high-altitude fighters.