The effects from government subsidies for heat pumps are diverse and I have a hard time sorting them into good/bad buckets:

• The environmental damage incurred within a country is reduced compared to the situation without the subsidy. (Although that is only true if the additional disposable income freed by the subsidy isn't used for environmentally harmful activities.) This benefits everyone, but especially low-income households who not only tend to live closer to toxic oil/gas infrastructure but also have less money for climate and environmental adaptation.
• Since richer people tend to have more CO2-intensive lives, the first people who are able to use the subsidy may actually some of the worst offenders.
• There is less pressure on the often imported goods gas/oil and less pressure on the scarce goods wood/coal. This may reduce their price, making them more affordable to poorer people. Conversely, it may also lead to economies of scale breaking down or the market situation forcing enough actors off the market that a monopoly forms, thus raising prices.
• There is a similar effect for heat pumps themselves: They may become more affordable due to economies of scale being realized. They may also be inflated in price due to the government subsidies allowing manufacturers to sell overpriced goods.
• Since poor people are neither home-owners nor in possession of enough money to be able to get the government subsidies, the subsidies clearly redistribute from the poor to the rich.
• Rentors will likely enjoy lower running costs for their heat (although its likely that their rent itself is increased at least in the initial years).

I would clearly favor an earlier, forced, unsubsidized phase-out for home-owners within certain income brackets ... but society has ways to make sure these things never happen (aka rich people's influence on media/politics). So subsidies for everyone it is, I guess.