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One of the column multi line text
Change this to a People/Group column that allows multi-select ("Allow multiple selections") and then filter for [Me]. [Me] must be a real user, and multi-line text columns are just text, not users.
If you want a short list of users to select from (not all users), create a SharePoint group ("Choose from") with just those ...
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[Me] only works for People column. The easiest way for your requirement is using Multi-people & group column to store the approvers instead of multi-line text column, then create a view and use [Me] to filter items.
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