Just getting started with this list.

Chat Service: TAWK.TO https://www.tawk.to/

Basic chat is free with Tawk and various upgrades are subscription based. Installation is a snap. After setting up the account they walk you through the "get started" steps and give you a snippet of js and then it simply works.

Slide Show / Carousel: https://swiperjs.com/

Swiper is modern replacement for BX Slider. Basic usage is super simple, and things can get as complex as you want them to because of the number of options available.

Some more info here: 

https://www.scotsscripts.com/mvblog/slider-swiperjs.html 

https://www.scotsscripts.com/mvblog/swiperjs-how-to-place-arrows-outside-of-related-products-style-slide-content.html

Newsletter Signup Service:

They all suck.

Project Management:

They should just use Github - https://docs.github.com/en/issues/tracking-your-work-with-issues/configuring-issues/planning-and-tracking-work-for-your-team-or-project

There are plugins for more advanced functionality.

Third Party Search

Algolia seems to be working well for a few clients. Have no idea about cost or setup: https://www.algolia.com/

Bootstrap 5 Icons 

Useful and works for most situations: https://icons.getbootstrap.com/