MySQLServer: Check if conditions exist in group, then label entire group - sql-server

Question

My goal is to add another column to an existing table, to see if the value/conditions exists in a group and appropriately labeling the entire group if it is present or not.
If a Team has one project with a budget >= 20M or Actual_Spend >=2.5M I want to label the Team and all it's projects as Table 1 in the Category column. Irrespective if the other projects within the same Team fit this criteria.
I will provide a SQL fiddle link w/ my solution: http://sqlfiddle.com/#!18/3ddaf/12/0
I'm ending up with two extra columns of "Team" and "Category" and not sure how they're ending up there.
Below is the end result I'm looking for. I'm open to better solutions than the one I provided.
Thank you for your time
| Team | ProjectID | Budget | Actual_Spend | State | Category |
|------|-----------|----------|--------------|------------|----------|
| Cyan | 2 | NULL | NULL | Utah | Table 1 |
| Blue | 1 | NULL | 3000000 | California | Table 1 |
| Cyan | 1 | 20000000 | 1000000 | Utah | Table 1 |
| Blue | 2 | 22000000 | NULL | California | Table 1 |
| Red | 1 | 7000000 | 1000000 | Washington | Table 2 |
| Red | 2 | 19999000 | 2490000 | Oregon | Table 2 |
| Gray | 1 | 19000000 | 2500000 | Utah | Table 1 |
| Gray | 1 | 10000000 | 500000 | Utah | Table 1 |
Providing code to create the dataset:
Create Table Source_Data
(
Team varchar(50),
ProjectID INT,
BUDGET INT,
Actual_Spend INT,
State varchar(max),
)
INSERT INTO Source_Data
VALUES
('Blue',1,NULL,3000000,'California'),
('Green',1,20000000,1000000,'Utah'),
('Blue',2,22000000,NULL,'California'),
('Green',2,NULL,NULL,'Utah'),
('Red',1,7000000,1000000,'Washington'),
('Red',2,19999000,2490000,'Oregon'),
('Yellow',1,19000000,2500000,'Utah'),
('Yellow',1,10000000,500000,'Utah');

Answer 1

I think that you are looking for window functions:
select
s.*,
min(case when Budget>=20000000 or Actual_Spend>=2500000 then 'Table1' else 'Table2' end)
over(partition by team) Category
from Source_Data s
If any of the records having the same team satisfies condition Budget>=20000000 or Actual_Spend>=2500000, the new column yields Table1, else it produces Table2.
Demo on DB Fiddle:
Team | ProjectID | Budget | Actual_Spend | State | Category
:--- | --------: | -------: | -----------: | :--------- | :-------
Blue | 2 | 22000000 | null | California | Table1
Blue | 1 | null | 3000000 | California | Table1
Cyan | 1 | 20000000 | 1000000 | Utah | Table1
Cyan | 2 | null | null | Utah | Table1
Gray | 1 | 19000000 | 2500000 | Utah | Table1
Gray | 1 | 10000000 | 500000 | Utah | Table1
Red | 1 | 7000000 | 1000000 | Washington | Table2
Red | 2 | 19999000 | 2490000 | Oregon | Table2