UPDATE: A Simpler Method, without the Chatter Notification:

max(record.seller_ids.mapped('delay'), default=3)

You can create a Python Code based Server Action:

Here a default lead time of 3 days will be used if a Vendor has not yet been added to the Product Purchase tab and there will be a Chatter Note added if a Vendor is found.

# custom_ray_odoo

# loop through all selected product(s)
for record in records:
    
    # set lead time to default 3 days
    lead_time = 3
    found_vendor = False
    
    # loop through all the vendor(s) on the purchase tab
    for vendor_price_line in record.seller_ids:
        if vendor_price_line.delay > lead_time:
            lead_time = vendor_price_line.delay
            found_vendor = vendor_price_line.partner_id.name
    
    # update the record
    record.update({
      'sale_delay': lead_time
    })
    
    if found_vendor:
      # notify via chatter
      body='Customer Lead Time updated to %s days based on %s' % (lead_time, found_vendor)
      record.message_post(body=body)

Note: Enterprise Customers - please contact your Odoo Digital Advisor or Odoo Partner if you want to add this customization to your database so it is fully supported. The code here is a prototype that does not support Product Variants and makes assumptions about how your database is setup. It won't necessarily work "as is" for all Users.