I wish I could be helpful with regard to sources, Sarushka, but I can't at the moment. But consider the following.
First, though volume, even in historiography, isn't everything, it should be taken into account. The only source alleged so far for Yurovsky's regret over his murder of Nicholas and his family is FOTR. The scholarship and reliability of that tome is seriously questionable, to put it mildly. No other source, (and I've read a hell of a lot), alleges any regret or repentance on Yurovsky's part
I believe it was Yurovsky's son Alexander who was the immediate personal source of his father's statement of regret. I have read (can't say where, Sarah) that he claimed the opposite, that his father was totally unrepentant.
In terms of what we might consider the internal consistency of Yurovsky's life, the conclusion would be that he did not feel regret.I think we all know , not only his views on Bolshevism/communism, but also on autocracy and monarchy More importantly, we know what he did, personally. That is, he was a consistent, ruthless servant of the Soviet state, proud of his loyalty and dedication. Regret over his murders of the IF is totally out of his character
For what it's worth , the case of his daughter Rimma confirms the above. She was as dedicated to the Party as her father, perhaps more. She was also dedicated to her father himself, as he was to her. As witness their great desire to meet again after her imprisonment.
Any putative regrets on Yurovsky's part would have to have been very belated, as we know he was one of the 'stars' of the 1934 reunion at Ipatiev House of the Romanov killers and Urals leadership from 1918. He spoke at length on that occasion, and ,let's be clear, this was a Bolshevik celebration and commemoration of their historic role in the brutal end of Tsarism and of the Romanov line. (recall that the murders of GD Elizabeth ,GD Serge Michailovich and the Konstantine princes at Alapaevsk took place within 24 hours of the IH slayings). Yurovsky was 56 years old by then and would have had a long time to evolve morally towards repentance.
It's not impossible that he felt regret when nearing death, but it's extremely unlikely. It certainly wouldn't have derived from any religious motive , as he had none. I'd certainly like to hear of any sources alleging his regret, but all I've heard is the questionable and contradictory statements of his son Alexander. If this latter had become aware of end-of-life remorse on his father's part, his status as a young Soviet naval officer would have made frankness and public acknowledgement of such very problematic.