tl;dr: The limit of 100 http callouts is the same for all transactions (be they synchronous or async).
The answer here resides in another piece of documentation: https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_gov_limits.htm
Salesforce gives us a semi-visual representation of which limits apply to both sync and async transacttions, and which ones have different limits for sync vs async. As I'm waiting for sfdx to do a large push, I'll try to capture the formatting of that document here.
+----------------------------------+--------------------------+--------------------------+
| Description | Synchronous Limit | Asynchronous Limit |
+----------------------------------+--------------------------+--------------------------+
| Total number of SOQL | |
| queries issued | 100 | 200
|
| Total number of |
| records retrieved
| by SOQL queries | 50,000
|
| Total number of records |
| retrieved by |
| Database.getQueryLocator | 10,000
|
| Total number of SOSL |
| queries issued | 20
|
| Total number of records |
| retrieved by a single |
| SOSL query | 2,000
|
| Total number of DML |
| statements issued | 150
|
| Total number of records |
| processed as a result |
| of DML statements, |
| Approval.process, |
| or database.emptyRecycleBin | 10,000
|
| Total stack depth for any |
| Apex invocation that recursively |
| fires triggers due to insert, |
| update, or delete statements | 16
|
| Total number of callouts |
| (HTTP requests or Web services |
| calls) in a transaction | 100
|
| Maximum cumulative timeout |
| for all callouts (HTTP |
| requests or Web services calls) |
| in a transaction | 120 seconds
|
| Maximum number of methods with |
| the future annotation |
| allowed per Apex invocation | 50
|
| Maximum number of Apex jobs |
| added to the queue with |
| System.enqueueJob | 50
|
| Total number of sendEmail |
| methods allowed | 10
|
| Total heap size | 6 MB | 12 MB
|
| Maximum CPU time on the | |
| Salesforce servers | 10,000 milliseconds | 60,000 milliseconds |
|
| Maximum execution time |
| for each Apex transaction | 10 minutes
|
| Maximum number of push |
| notification method |
| calls allowed per Apex |
| transaction | 10
|
| Maximum number of push |
| notifications that can be |
| sent in each push |
| notification method call | 2,000 |
+----------------------------------+--------------------------+--------------------------+