Hi Jonathan,

>> https://salesforce.stackexchange.com/questions/121123/how-to-restrict-file-type-in-standard-page-attach

In the above link there is a implementation that you can use I am adding it below for quick reference:
 

Here is how I able to solve the above issue:

public static final List<string> CONTENT_TYPES = new string[]{'image/gif','image/png','image/jpg'};

for(attachment a: Trigger.new)
{
   if (!isAllowedContentType(a.ContentType)) {
       a.addError('only allowed jpg, gif, png files');
   }    
}
Private helper method:

   private static boolean isAllowedContentType(string selCT)
   {
      for(String ct : CONTENT_TYPES) 
      {
          if(ct == selCT) {
            return true;
          }
      } 
      return false; 
   }

If you are building custom lightning component implementation then as mentioned in the documentation https://developer.salesforce.com/docs/component-library/bundle/lightning-file-upload/documentation you can make use of acceptedformats using accept attribute to the tag as implemented in the below snippet:
 

<template>
    <lightning-file-upload
            label="Attach receipt"
            name="fileUploader"
            accept={acceptedFormats}
            record-id={myRecordId}
            onuploadfinished={handleUploadFinished}
            multiple>
    </lightning-file-upload>
</template>

import { LightningElement, api } from 'lwc';
export default class FileUploadExample extends LightningElement {
    @api
    myRecordId;

    get acceptedFormats() {
        return ['.pdf', '.png'];
    }

    handleUploadFinished(event) {
        // Get the list of uploaded files
        const uploadedFiles = event.detail.files;
        alert("No. of files uploaded : " + uploadedFiles.length);
    }
}

>> https://help.salesforce.com/articleView?id=000319977&type=1&mode=1

As mentioned in the above if you want to restrict the upload of specific type to chatter you can use the trigger and add to the condition the necessary file types that aren't allowed.

Let me know if it helps you and close your query by marking it as solved so that it can help others in the future.  

Thanks.