A Jira link only works for someone with an Atlassian account, access to your site, and browse permission on that project. External people have none of those by default, so they hit a login wall or a 'you don't have permission' error. The options are to license them, use guest access on a paid plan, or send the information rather than the link.
If everyone in your company can see your Jira project, it's almost always because the Browse Projects permission is granted to 'Any logged-in user' in the project's permission scheme. That default makes the project visible to every licensed user in your site. Change that grant to a specific project role or group and the exposure stops.
A Jira permission scheme is just a reusable list of 'who can do what,' attached to one or more projects. Most permission confusion traces to a single setting — the Browse Projects permission granted to 'Any logged-in user' — which quietly lets everyone in your instance see a project. Understand roles vs groups, fix that one default, and permission schemes stop being scary.
Jira Cloud has no guest role. Every account that can see a project consumes a licensed seat, with one narrow exception (the Jira Service Management customer portal). Everything else people call 'guest access' is one of three workarounds: automation emails, anonymous public access, or a sharing app. Which you want depends on whether your guest needs to work in the project or just see it.