Still not their fault. Your mistake was making plans before everything was done. It sucks, I get that. But "playing", "lazy", etc... nah.
These are the correct words and expressions.
Pandemic.
Reduced capacity in some departments while spreading personell resources to departments that need them more.
Fulfilling obligations towards current TFW, PRs, and Citizens to support them during the pandemic.
Yes, we have a right to receive a PR card. We do not have a right to receive it NOW. We have the right to receive it as fast as they can process it with the resources they have. If it's an inconvenience to you it's because your plans made it an inconvenience to you. The pandemic has been ongoing for a year now. Making plans for non-essential travel during a pandemic, when the government is recommending against it..... that's kind of stupid.