Existing orders were delayed to October. New orders are January-February 2022.
The refreshed Tesla Model X and Model S are noticeably delayed. The first cars were expected in February 2021, but instead of that, we saw only how the delivery dates for new orders move further away.
Customers that placed orders early report that Tesla updated delivery timelines of the Model S, asking for patience. In the case of Model X, the expected delivery date is now moved to October according to the latest reports (via Teslarati). It does not sound like the promised "very shortly."
It's a clear sign that Tesla has some issues with launching the new Model S/X. None were produced in the first quarter of this year. The nature of the problem remains unknown - it might be supply chain, but it might be related to other things as the refresh was quite comprehensive.
The Model S might appear on the market within several weeks or months, while the Model X is expected to follow after the S. There is a risk that if delays will extend further, the new Model X will not enter the market in 2021 (new orders are expected in January-February 2022 already).
It's quite unfortunate for Tesla that after a period of decreasing sales of Model S/Model X, with many new competitors in the high-end segment, the refresh is not progressing smoothly.
With the target of 2,000 units per week (or roughly 100,000 a year) after a ramp-up phase, and an average price of $100,000 or so, a multi-month delay is very costly to Tesla. Annual revenues from the S/X have potential of up to over $10 billion.