My impression is that in co-located work mentality, outsourcing was hindered by needing the outsourced team to be distant. Has Covid-based change in effectiveness of remote work effectiveness, has outsourcing actually increased. Are there any statistics available on that.
Probably, however I doubt it can be accurately analyzed yet. In addition to many laid-off workers considering the freelancer economy, you are correctly observing that companies are considering temporary and remote workers to handle spikes in business as customers return in fits and spurts. This is not a settled state. And there are always risks with outsourcing.
It will take considerably more time before a meaningful set of data can be analyzed to produce statistics. Right now all data is going to be anomalous because no one has settled into a permanent pattern.