[8.13] Add synthetic serverless doc links (#182740) (#182976)

# Backport

This will backport the following commits from `main` to `8.13`:
- [Add synthetic serverless doc links
(#182740)](#182740)

<!--- Backport version: 9.4.3 -->

### Questions ?
Please refer to the [Backport tool
documentation](https://github.com/sqren/backport)

<!--BACKPORT [{"author":{"name":"Brandon
Morelli","email":"brandon.morelli@elastic.co"},"sourceCommit":{"committedDate":"2024-05-08T17:09:49Z","message":"Add
synthetic serverless doc links (#182740)\n\n## Summary\r\n\r\nAdds
Synthetic Serverless doc links (and one missing logs
link).\r\n\r\nCloses
elastic/obs-docs-team#219:
kibanamachine
<42973632+kibanamachine@users.noreply.github.com>\r\nCo-authored-by:
DeDe Morton
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synthetic serverless doc links
","number":182740,"url":"#182740
synthetic serverless doc links (#182740)\n\n## Summary\r\n\r\nAdds
Synthetic Serverless doc links (and one missing logs
link).\r\n\r\nCloses
elastic/obs-docs-team#219:
kibanamachine
<42973632+kibanamachine@users.noreply.github.com>\r\nCo-authored-by:
DeDe Morton
<dede.morton@elastic.co>","sha":"e7a9291bb97d7a3bdef947ed8f8c39d8cc4c3a56"}},"sourceBranch":"main","suggestedTargetBranches":["8.13","8.14"],"targetPullRequestStates":[{"branch":"8.13","label":"v8.13.0","branchLabelMappingKey":"^v(\\d+).(\\d+).\\d+$","isSourceBranch":false,"state":"NOT_CREATED"},{"branch":"8.14","label":"v8.14.0","branchLabelMappingKey":"^v(\\d+).(\\d+).\\d+$","isSourceBranch":false,"state":"NOT_CREATED"},{"branch":"main","label":"v8.15.0","branchLabelMappingKey":"^v8.15.0$","isSourceBranch":true,"state":"MERGED","url":"#182740
synthetic serverless doc links (#182740)\n\n## Summary\r\n\r\nAdds
Synthetic Serverless doc links (and one missing logs
link).\r\n\r\nCloses
elastic/obs-docs-team#219:
kibanamachine
<42973632+kibanamachine@users.noreply.github.com>\r\nCo-authored-by:
DeDe Morton
<dede.morton@elastic.co>","sha":"e7a9291bb97d7a3bdef947ed8f8c39d8cc4c3a56"}}]}]
BACKPORT-->

Co-authored-by: Brandon Morelli <brandon.morelli@elastic.co>

packages/kbn-doc-links/src/get_doc_links.ts

@@ -575,21 +575,33 @@ export const getDocLinks = ({ kibanaBranch, buildFlavor }: GetDocLinkOptions): D
         ? `${SERVERLESS_OBSERVABILITY_DOCS}create-custom-threshold-alert-rule`
         : `${OBSERVABILITY_DOCS}custom-threshold-alert.html`,
       monitorStatus: `${OBSERVABILITY_DOCS}monitor-status-alert.html`,
-      monitorUptime: `${OBSERVABILITY_DOCS}monitor-uptime.html`,
+      monitorUptime: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}monitor-synthetics`
+        : `${OBSERVABILITY_DOCS}monitor-uptime.html`,
       tlsCertificate: `${OBSERVABILITY_DOCS}tls-certificate-alert.html`,
       uptimeDurationAnomaly: `${OBSERVABILITY_DOCS}duration-anomaly-alert.html`,
-      monitorLogs: `${OBSERVABILITY_DOCS}monitor-logs.html`,
+      monitorLogs: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}discover-and-explore-logs`
+        : `${OBSERVABILITY_DOCS}monitor-logs.html`,
       analyzeMetrics: isServerless
         ? `${SERVERLESS_OBSERVABILITY_DOCS}infrastructure-monitoring`
         : `${OBSERVABILITY_DOCS}analyze-metrics.html`,
-      monitorUptimeSynthetics: `${OBSERVABILITY_DOCS}monitor-uptime-synthetics.html`,
+      monitorUptimeSynthetics: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}monitor-synthetics`
+        : `${OBSERVABILITY_DOCS}monitor-uptime-synthetics.html`,
       userExperience: `${OBSERVABILITY_DOCS}user-experience.html`,
       createAlerts: isServerless
         ? `${SERVERLESS_OBSERVABILITY_DOCS}alerting`
         : `${OBSERVABILITY_DOCS}create-alerts.html`,
-      syntheticsAlerting: `${OBSERVABILITY_DOCS}synthetics-settings.html#synthetics-settings-alerting`,
-      syntheticsCommandReference: `${OBSERVABILITY_DOCS}synthetics-configuration.html#synthetics-configuration-playwright-options`,
-      syntheticsProjectMonitors: `${OBSERVABILITY_DOCS}synthetic-run-tests.html#synthetic-monitor-choose-project`,
+      syntheticsAlerting: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}synthetics-settings#alerting`
+        : `${OBSERVABILITY_DOCS}synthetics-settings.html#synthetics-settings-alerting`,
+      syntheticsCommandReference: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}synthetics-configuration#playwrightoptions`
+        : `${OBSERVABILITY_DOCS}synthetics-configuration.html#synthetics-configuration-playwright-options`,
+      syntheticsProjectMonitors: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}synthetics-get-started-project`
+        : `${OBSERVABILITY_DOCS}synthetic-run-tests.html#synthetic-monitor-choose-project`,
       syntheticsMigrateFromIntegration: `${OBSERVABILITY_DOCS}synthetics-migrate-from-integration.html`,
       sloBurnRateRule: isServerless
         ? `${SERVERLESS_OBSERVABILITY_DOCS}create-slo-burn-rate-alert-rule`
@@ -932,7 +944,9 @@ export const getDocLinks = ({ kibanaBranch, buildFlavor }: GetDocLinkOptions): D
       apiKeyPrivileges: `${SERVERLESS_DOCS}api-keys#restrict-privileges`,
     },
     synthetics: {
-      featureRoles: `${OBSERVABILITY_DOCS}synthetics-feature-roles.html`,
+      featureRoles: isServerless
+        ? `${SERVERLESS_OBSERVABILITY_DOCS}synthetics-feature-roles`
+        : `${OBSERVABILITY_DOCS}synthetics-feature-roles.html`,
     },
     telemetry: {
       settings: `${KIBANA_DOCS}telemetry-settings-kbn.html`,