The currently available information shows mixed evidence. But the vaccine campaign began in December/January 2021. Back then, BioNTech's CEO believed the protective effect would last "for at least a year"[1] (Booster shots gained traction in April/May [2], though they were mainly presented as a way to protect against new variants, not waning immunity in general).
Waning immunity was never really a topic (until now). You can also see its complete disregard in the "EU Digital COVID Certificate" [3]. Recovered persons are exempt from restrictions for 180 days, fully vaccinated persons indefinitely.
[1] https://www.reuters.com/article/us-health-coronavirus-vaccin...
[2] https://www.cnbc.com/2021/04/15/pfizer-ceo-says-third-covid-...
[3] https://ec.europa.eu/info/live-work-travel-eu/coronavirus-re...