Finalization of the site on Magento 2 - optimization of performance and stabilization of checkout after migration

There is an online store for spare parts for agricultural machinery on Magento 2.4.6-p3 (PHP 8.2, MySQL 8, Elasticsearch), AWS Lightsail hosting, Cloudflare CDN. After migrating from another VPS, the site became slower, and the delivery and payment methods for certain combinations of city and basket weight periodically disappear in the checkout. The number of 500 errors under load also increases, and the time to the first byte on categories sometimes exceeds 2-3 seconds. It is necessary to conduct a technical audit, find the reasons and make revisions with a focus on productivity and reliability of ordering.

Environment and access - staging and production, Git repository with CI via GitHub Actions, deployment via SSH. Installed third-party modules for delivery (Nova Poshta API), payment (LiqPay), filtering (Amasty), caching currently only Full Page Cache Magento, Redis is not configured.

Expected result
- Stable checkout without disappearing delivery and payment methods, correct operation of delivery rules by weight and city
- Noticeable acceleration of categories and product cards without breaking indexing and searching
- Reduced 500 errors under load and predictable cache behavior

What to do (steps)
1) Audit and reproduction of the checkout problem - analysis of Magento, Nginx, PHP-FPM, MySQL slow log, Cloudflare logs, verification of the configuration of delivery and payment modules, reproduction of staging cases with recording of steps and data
2) Performance diagnostics - profiling (Magento profiler, Xdebug/Blackfire if possible), analysis of requests to the database, checking of indexes, evaluation of the impact of third-party modules, checking of the cache and operating modes (developer/production)
3) Refinement - correction of logic/configuration that leads to incorrect delivery/payment methods, point optimizations (queries, indexes, caching), Redis settings for cache and sessions, adjustment of PHP-FPM/Nginx parameters to the current server resource, without changing the design
4) Verification and release - regression on staging, preparation of migration of configs, deployment in production with minimal downtime, short technical instructions on what was changed and how to check

Limitation
- We do not change the theme and layout, we do not update Magento to a new major version
- We do not disable critical business modules (delivery, payment, filters), we can offer alternatives only if there is proof of a causal relationship
- Any changes only through Git and with the possibility of rollback

Acceptance criteria (measurable)
- On staging, the cause of the checkout problem was recreated and a fix was added, which removes the problem in 20 consecutive test checkouts for 3 cities and 3 weight ranges, with LiqPay and Nova Poshta
- TTFB for category pages on production with a warmed-up cache of no more than 800 ms in the 90th percentile (measurement via WebPageTest or Lighthouse with a fixed location)
- Under the load of 30 simultaneous users for 10 minutes (k6 or similar), the share of 5xx responses is no more than 0.5%, the average response time for cached pages is no more than 400 ms
- Reported: root cause found, list of changes, commands/settings applied, and instructions on how to repeat the tests

Experience with Magento 2, checkout debugging, MySQL optimization, Redis, PHP-FPM/Nginx, and working with Cloudflare is expected.