Does the 67w USB-C charger do no support fast charging for MacBook Pro 14' 2021

Correct.

The base model that includes the 67W charger does not support fast charging.

You need to optionally add the 96W USB-C Power Adapter.

Apple recommends pairing this power adapter with your 14-inch MacBook Pro (2021) using a USB-C to MagSafe 3 Cable or USB-C Charge Cable to take advantage of fast charging, so you can go from 0 to 50 percent charge in around 30 minutes.

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Please refer to: Fast charge your 14-inch or 16-inch MacBook Pro - Apple Support.

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