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Summary of Significant Accounting Policies - Revenue Recognition (Details) - USD ($)
$ in Thousands
 12 Months Ended
May 15, 2023
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Total revenues   $ 193,920 $ 236,164 $ 199,980  
Percent of construction supervision   5.00%      
Property management fees revenue   $ 76,444 63,153 59,667  
Property management fee   $ 15,641 18,443 16,743  
Tremont Advisors          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Incentive fee percentage condition 1   20.00%      
Incentive fee percentage condition 2   7.00%      
Minimum          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Percent of gross collected rents   2.50%      
Maximum          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Percent of gross collected rents   3.50%      
Termination and incentive business management fees          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Total revenues $ 45,282   45,282    
Advisory services          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Total revenues   $ 4,506 4,520 4,530  
Advisory services | Tremont Advisors          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Management fee percentage pursuant to agreement   1.50%      
Total revenues   $ 4,506 4,520 4,530  
Termination and incentive fees | Tremont Advisors          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Total revenues   $ 1,213 660 0  
Total Managed Equity REITs          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Percentage of historical cost of transferred real estate assets   0.50%      
Percentage of average invested capital below threshold limit   0.70%      
Threshold amount, maximum   $ 250,000      
Percentage of average invested capital above threshold limit   0.50%      
Threshold limit, minimum   $ 250,000      
Percentage of average market capitalization below threshold limit   0.70%      
Percentage of average market capitalization above threshold limit   0.50%      
Aggregate annual base business management fees   $ 84,182 85,603 96,031  
Incentive management fee percentage   12.00%      
Aggregate incentive business management fees     0 0 $ 0
Total revenues   $ 134,882 139,215 148,094  
Managed Operating Companies          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Management fee percentage pursuant to agreement   0.60%      
Managed Public Real Estate Capital          
New Accounting Pronouncements or Change in Accounting Principle [Line Items]          
Aggregate annual business management fees   $ 27,575 36,815 39,653  
Total revenues   $ 140,648 $ 199,617 $ 168,550