I'm not really convinced that's true on any counts. As awful as the lockdown restrictions were, it's extremely unlikely that either party will be faced with similar issues in the next 5 years, and even more unlikely that UK governments or the wider international community would be would accept lockdowns even if we did. People definitely vote on more than one issue, and it's unlikely that lockdowns will be foremost in peoples minds. Even if people are looking back to 2020, the Tories were squarely responsible for more long-term damage to lives and the economy from hard Brexit in the same period, and that's ongoing in a more apparent way.
In terms of how Starmer would have reacted if he'd actually been in government, I don't think the Tories actually did anything more more positive in that respect - we actually pretty long lockdowns compared to some other countries. It was Sunak who introduced and failed to time-limit the overly-generous furlough scheme, and hard-man Hancock who decided that his best bet was to ignore all the evidence of lockdown harms rather than make a balanced decision.
I'm angry about the whole situation, and angry that it was only really extreme right-wing parties across Europe who found themselves able to take a sane approach to the situation. However, in terms of mainstream parties who are likely to win elections anywhere in Europe, I'm not sure you could get a fag paper between the Covid approaches of virtually any of them.