Stockholders' and Members' Equity - Narrative (Details) $ / shares in Units, $ in Thousands				3 Months Ended			9 Months Ended		12 Months Ended
	Oct. 02, 2023 intallment shares	Oct. 01, 2023 intallment shares	Feb. 23, 2021 shares	Jun. 30, 2023 USD ($) $ / shares shares	Mar. 31, 2023 USD ($)	Jun. 30, 2022 USD ($)	Jun. 30, 2023 USD ($) $ / shares shares	Jun. 30, 2022 USD ($) shares	Mar. 31, 2023 USD ($) shares	Mar. 30, 2022 USD ($)
Share-Based Payment Arrangement [Abstract]
Percentage of expected performance targets to be achieved target award				80.00%			80.00%
Authorized amount | $										$ 50,000
Repurchase and retirement of shares amount | $					$ 1,579
Stock repurchase program, remaining authorized repurchase amount | $				$ 48,100			$ 48,100
Equity-based awards | $							7,185	$ 7,274
Employee stock purchase plan
Share-Based Payment Arrangement [Abstract]
Equity-based awards | $				200			600
Stock to be purchased under ESPP | $							$ 1,000
Performance Shares
Share-Based Payment Arrangement [Abstract]
Awarded (in shares) | shares							83,036
Percentage of target award granted							100.00%
Number of shares of common stock consisted in each unit (in shares) | shares							1
Share-based payment arrangement, expense | $				900		$ 1,300	$ 3,000	$ 4,000
Performance Shares | Forecast
Share-Based Payment Arrangement [Abstract]
Awarded (in shares) | shares	69,748	13,288
Number of equal annual installments for vesting | intallment	3
Time-Based Restricted Stock Units
Share-Based Payment Arrangement [Abstract]
Awarded (in shares) | shares								133,735
Time-Based Restricted Stock Units | Forecast
Share-Based Payment Arrangement [Abstract]
Awarded (in shares) | shares	111,185	22,550
Number of equal annual installments for vesting | intallment		3
Restricted Stock Units
Share-Based Payment Arrangement [Abstract]
Awarded (in shares) | shares							216,771,000
Share-based payment arrangement, expense | $				1,900		$ 2,500	$ 6,600	$ 7,300
Nonvested award | $				$ 5,700			$ 5,700
Cost not yet recognized, period for recognition							1 year 3 months 18 days
Employee stock purchase plan
Share-Based Payment Arrangement [Abstract]
Shares issued as part of employee stock purchase plan (in shares) | shares							43,692
Shares issued (in shares) | $ / shares				$ 24.31			$ 24.31
Class A Common Stock
Share-Based Payment Arrangement [Abstract]
Capital shares reserved for future issuance (in shares) | shares				1,574,646			1,574,646
Repurchased and retired shares (in shares) | shares							63,353		73,487
Repurchase and retirement of shares amount | $							$ 1,600		$ 1,900
Percentage of outstanding shares, ESPP issuance			1.00%
Class A Common Stock | Maximum
Share-Based Payment Arrangement [Abstract]
Shares issued as part of employee stock purchase plan (in shares) | shares			449,257