[Tracking][Binlog] Binlog feature umbrella — all sub-issues tracked here

### BackGround
Doris Stream is a core feature designed to break through the bottleneck of full-table computation in traditional ETL and to unify stream and batch processing. By introducing the concept of Table Stream, it effectively tracks row-level data changes (inserts, deletes, updates) on source tables, enabling downstream tasks to perform incremental computation only on the changed data. This significantly boosts data processing efficiency, cuts compute resource consumption, and dramatically reduces the latency from data ingestion to analytics — providing powerful engine-level support for building near-real-time data warehouses.

This is the Bug Tracking link. All issues will be listed in this link.

### Bug List

- [x] #65309
- [x] #65339
- [x] #65383
- [x] #65388
- [ ] #65389
- [x] #65390
- [x] #65705
- [ ] #65865
- [ ] #65866
- [ ] #65897
- [x] #65901
- [x] #65947
- [x] #65951
- [x] #65976
- [x] #66368
- [x] #66390
- [x] #66537

### Correctness issues
- [x] #67091
- [ ] #67092
- [x] #67093
- [x] #67094
- [x] #66273
- [x] #66287
- [x] #66338
- [x] #67095
- [x] #67096
- [ ] #67097
- [ ] #67098
- [ ] #67099
- [x] #67100
- [x] #67101
- [x] #67102
- [ ] #67103
- [ ] #67104
- [ ] #67105
- [x] #67106
- [ ] #67107
- [ ] #67108
- [ ] #67109
- [x] #67443

This issue is a tracking umbrella for the Doris Stream Binlog work rather than a self-contained change. Start by reviewing the unchecked sub-issues listed under Bug List and Correctness issues, then follow the specific issue that defines an actionable task. Done means the selected sub-issue is resolved and its checkbox is updated here.

Written by the indexing model from the issue text.