Odoo support told me that this behavior is expected because standard_price is a company-dependent field. But I found a workaround with automated actions that did the trick for me:

companies = [1,2,4] # all companies that should get the same standard_price
companies.remove(env.company.id) # remove the active company from list
for target in companies:
  targetrecord = record.with_company(target)
  if targetrecord.standard_price != record.standard_price:
    targetrecord['standard_price'] = record['standard_price']

If you create a product with company field empty, this product will be used from every company. This rule is valid for every model in Odoo. So, if you want to share something between companies, leave the company field empty.