No Ukraine didn't complain, two un-named government officials complained with no confirmation from the Ukraine government. If Starlink was "Catastrophically crashing" because of shenanigan's by Musk I would have quickly expected to see official confirmation from the Ukranian government of Starlink issues around areas recently liberated. The Ukrainian government hasn't been shy about directly going after Musk publicly if necessary for doing something stupid. Has this happened?
Two government officials, speaking under the condition of anonymity, told the publication that soldiers had difficulty connecting to the satellite internet service when they entered cities that had only recently been freed from Russian troops.
One government official from Ukraine said that the outages have caused a "catastrophic" loss of communication between the country's military forces. Another official said the lack of internet connection resulted in panicked calls from troops to help lines, FT reported.
I would also draw your attention to this paragraph from the same article.
Roman Sinicyn, a co-ordinator at a foundation that donates Starlink systems to the Ukrainian armed forces, told FT the issue could be caused by SpaceX representatives working to make sure Russian soldiers couldn't use the technology, as the liberation of some of the areas had not been made public yet at the time of the connectivity issues.