[Partners] Verify if a user can send some proposal in the 'Стати партнером' modal window

**Priority:**
High

**Steps to reproduce**
1. Go to the site.
2. Click on the Burger menu and 'Партнери' button.
Or scroll down to the footer and 'Партнери'.
3. Scroll down and click on the 'Стати партнером' button in the center of the page.
4. Fill in the email field and proposal or idea field (e.g. "o@g.ua" and "Test").
5. Check the captcha and click on the 'Відправити' button.
6. Repeat steps 4-5 using the 'Стати партнером' button located at the bottom right.

**Expected result**
1. The modal window is closed.
2. The 'Лист успішно надісланий' message appears top of the page.

**User story:**
#136

Reproduce the submission flow from the Partners page, testing both “Стати партнером” buttons with the stated email, proposal, and captcha steps. Verify that the modal closes and “Лист успішно надісланий” appears after each submission; the issue does not name a file or test to inspect.

Written by the indexing model from the issue text.