Yes, paragraph 7 of Schedule 1 of the Elections Act 2022 amended the Representation of the People Act 1983 to include a requirement for the Secretary of State to publish a report on the effect of voter ID on the May 2023 local elections and the next two parliamentary elections.
It also, in paragraph 24, amended the elections rules to introduce a duty for the various officers involved in the election - the presiding officer, the returning officer, and the registration officer - to collect and anonymise prescribed information relating to applications for ballot papers made under the new voter ID rules in order to inform the Secretary of State's report.
Furthermore, the Electoral Commission has undertaken to conduct public opinion research to evaluate the effect on those who do not attend a polling station to be counted, according to Cat Smith, a member of the Speaker's Committee on the Electoral Commission:
Jeff Smith: It is good news that data will be collected on the number of voters who get turned away for not having ID at a polling
station, but as we all know, parties often have tellers outside who
will remind people about the voter ID requirements, so how can the
Electoral Commission collect data on voters who turn away before they
even get into the polling station?
Cat Smith: My hon. Friend, who is a seasoned campaigner and is familiar with the scenes outside polling stations, has identified the
potential gap in the data. Of course, polling station staff will not
be able to collect data from people who do not go into the polling
station. However, the commission has identified that as a potential
issue and will undertake public opinion research on the reasons why
people did or did not vote in the elections.
So yes, data on those affected by the new rules will be collected, and the information published after the May 2023 local elections, as well as the next two parliamentary elections. This will presumably take a similar form to the government's report on the 2019 voter ID pilot.