To add a watermark to multiple videos at once, you can use a video editing software that supports batch processing. Here are the steps to add a watermark to multiple videos using Adobe Premiere Pro:
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Open Adobe Premiere Pro and create a new project.

Import the videos that you want to add the watermark to by going to File > Import.

Create a new sequence by going to File > New > Sequence. Choose the sequence settings that match the resolution and frame rate of your videos.

Drag the videos from the Project panel to the timeline.

Add the watermark to the video by adding a logo or image overlay to the video. To do this, import the image or logo you want to use as the watermark by going to File > Import. Then, drag the image or logo to the timeline on a new video track above the main video track.

Adjust the size, position, and opacity of the watermark as desired by selecting the watermark on the timeline and adjusting the settings in the Effects Control panel.

Once you have the watermark set up the way you want it, select all of the videos in the Project panel that you want to add the watermark to.

Right-click on the videos and choose "Export Media" from the context menu.

In the Export Settings window, choose the output format and encoding settings that you want to use.

Under the "Output" tab, choose a destination folder where the watermarked videos will be saved.

Under the "Effects" tab, make sure that the "Video Watermark" checkbox is selected and that the watermark image or logo is selected in the dropdown menu.

Click "Export" to begin the batch export process. Adobe Premiere Pro will process each video in the batch and add the watermark to each one before saving the watermarked videos to the destination folder.