Climbing down the chain to retrieve the first secret, as shown here, worked consistently for me in the remaster. If you're having trouble with it, or just want to try something different, here's another way:

Crawl backwards out of the duct and hang onto the climbable wall.

Press Look to move the camera behind Lara. Then climb down until Lara is hanging just above the alcove with the golden rose. If you like, you can quick-save here. Just be sure to hold Action when reloading so Lara doesn't fall. This next bit may take a few attempts.

Press and release Back/Down to climb down a little at a time. When Lara's feet come off the wall, and she's hanging by her hands only...

...press and release Back/Down once more, so she descends a little further.

You should see Lara slide forward just a little, so her hands disappear into the wall. Her shadow should be visible on the floor of the alcove. If this doesn't happen, climb up a little then back down until it does.

Let go to land inside the alcove with the golden rose (9) (208/239) (SECRET #1, 31/36).

Once you have it, take a standing jump back to the bottom of the chain. Continue following the main walkthrough.
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