The chicken and the pig fable, along with the entire "chicken" and "pig" terminology, has been removed from the Scrum Guide.
The purpose of the Daily Scrum is for the Development Team to review and coordinate their activities. That is, the look at how they are doing towards completing the work in the Sprint Backlog and how they are doing toward achieving the Sprint Goals. One rule of the Daily Scrum is that only Development Team members participate and the Scrum Master ensures that attendees from outside the Development Team do not disrupt the event.
So, who is a Development Team member? The three Scrum roles are Product Owner, Scrum Master, and Development Team. The Development Team "consists of professionals who do the work of delivering a potentially releasable Increment of “Done” product at the end of each Sprint." Who this is depends on your organization. If your Business Analysts are doing work that is required to meet your team's Definition of Done, then they are part of the development team. However, if they aren't doing the work that goes into meeting the Definition of Done, then they aren't a member of the Development Team.
In the question, there are four roles for a Business Analyst listed:
- Gathering requirements by managing relationships with stakeholders and facilitating those conversations;
- Providing guidance on what to build when to release as much value as possible as early as possible;
This is part of the ongoing activity of refining the Product Backlog. This isn't tied to the Sprint, but the changing needs of the various stakeholders. This doesn't really have a place in Daily Scrum. Items should be added, removed, and reordered in the Product Backlog continuously, by the people who are empowered to make those decisions. That likely includes the Business Analysts.
- Helping the Scrum team to plan and improve their ways of working through retrospectives;
This isn't part of a Daily Scrum, but the Retrospectives. The Retrospective is open to the entire Scrum Team, which includes the Product Owner. If the Business Analysts are working closely with the Product Owner to support the team, it makes sense that they would also likely be present.
- Ensuring the work done by the team aligns with the wider business strategy.
This could potentially be useful at the Daily Scrum. As an observer, the Business Analysts can bring any possible delays in meeting the Sprint Goals and completing the Sprint Backlog out into planning for future work. In the event that the Sprint Goals are at risk, they can be available immediately following the Daily Scrum to coordinate with the team on how to prioritize the remaining work to add the most value to stakeholders. Although the Daily Scrum is timeboxed to 15 minutes, it's not uncommon to immediately move into more detailed discussions with the right people present following a Daily Scrum.
Per Scrum, BAs are not participants in the Daily Scrum unless they are also doing work toward achieving the Definition of Done. However, participation and attendance are different. You need to evaluate if having your BAs attend and then be available for discussions (as needed) after your Daily Scrum is worth their time.