Other people will be able to read quoted replies (including in browser clients) even if they can’t send one back to you. Don’t worry about using quoted replies before everyone else in your tenant has access to the feature. My reading is that the preview announcement is for people who want to use quoted replies early before general availability reaches their tenant. MC285886 only covers the Teams desktop clients. The preview announcement covers preview availability for the Teams desktop clients (Windows, Mac, and Linux) with the promise that quoted replies will soon be available for the Teams browser clients. The announcement is also covered in Microsoft 365 message center notification MC285886 ( roadmap item 81113), which says that the feature roll-out starts in mid-September and should be complete in early October.
On September 17, Microsoft announced the availability of quoted replies for chat messages for all users configured to use Teams public preview (the cool kids with the P beside their user photo). Now in Preview for Teams Desktop with Browser Support Soon