The USSR continued to produce SVT-40 until the end of the war. A total of 1,7-1,8 million were produced. Certainly not in the amount that they wanted before the war. The plan was 1,8 million in 1941 and 2,0 million in 1942.The only country that replaced bolt action rifles completly was the USA.
The soviet had the svt40 but switch back to the bolt action mosin nagant after the huge looses in 41.
Germany startet with the g43 rifle and the sturmgewehr 43-44 from ~43 on but cant produce enough.
I dont know any attempt of the british, italien or japanese of any self loading rifle.
France was in reasearch and testing but didnt put anything in production befor germany knocked at the border.
Interestingly france planed to equipe only combattroops with a self loading rifle. All others support troops who not should be direct combat with enemy troops should get the easy to produce MAS 36 as their weapons cause they dont need expesive self loading rifles. Its an interesting choice.
Italy and Japan have tried. Italy had many prototypes of self-loading rifles, formally one model was adopted. There was even a prototype based on a copy of the SVT-40.
The Japanese tested Pedersen rifle and Pedersen's copies. Also, at the end of the war, they tried to copy the M1 Garand.