Essentially this issue was raised last year in R (AB) v SSHD  EWHC 287 (Admin). The claimant, AB, is an Afghan national who sought entry to the UK under the Afghan Relocation and Assistance Policy (ARAP). She alleged for the judicial review that the UK government discriminated against her, contrary to Articles 8 and 14 of the European Convention on Human Rights, because ARAP was more procedurally demanding than the Ukrainian Family Scheme.
Although the difference in availability of the two schemes is not strictly because of nationality, the reality is that ones nationality is very closely connected to which scheme, if either, one can use. This entails the court applying a higher degree of scrutiny to the government's actions.
In this instance, the judge found that there was differential and unfavorable treatment of AB compared to a hypothetical Ukrainian comparator. However, she also said that the government was justified in operating different rules for different countries of origin. This was based on evidence from civil servants about the UK's national security posture, diplomatic links, and foreign policy objectives. For example, the UK is more worried about accidentally letting in an Afghan terrorist than a Ukrainian one, and the required background checks are correspondingly different. The judgment does not go into much detail here, but the overall legal point is that discriminatory treatment can potentially be justified if the grounds are sufficiently compelling.
The Equality Act 2010, raised in the question, might ordinarily be thought to apply to decisions by government about the provision of services. However, it is expressly disapplied as far as discrimination on the grounds of nationality, ethnic or national origin, in relation to decisions made under the Immigration Acts. (This term encompasses the several differently-named pieces of primary legislation relating to immigration, and the various rules and schemes made under them.) This is in section 17 of Schedule 3.
The Homes for Ukraine scheme would also be covered by this exemption, because it's part of the system for sponsoring people under the Ukraine Sponsorship Scheme (a different way that they can get visas).