alt Hacker NewsNo.
1. "Postponed" is not "cancelled"
2. "Postponed" is entirely normal within British politics. For most of my life, even the timing of general elections were at the whim of the government.
3. Given how Starmer polls, the delay is almost certainly going to make things un-favourable for him. Also unfavourable for Labour, unless they kick him out first.
Not that it would matter much if your conspiracy theory held water, given that one of the many constitutional problems the UK has is that local councils have negligible power (options are tied all over the place) and therefore local elections are functionally little more than opinion polls done in a voting booth.
"My conspiracy theory" is a set of facts that you and the source you cited (whose so-called "fact check" was mostly attempting to put into context) find really inconvenient. Fact 1: Starmer and his party are polling badly. Fact 2: Starmer and his party delayed several local elections, many of which were in constituencies where they currently hold power and won't afterward. This is not a good set of facts, regardless of how little those elections matter.