See Q & A #8 (page 11) on this TEA document:
CARES Act Funding and COVID Expense Reimbursement FAQ June 4, 2020
https://tea.texas.gov/sites/default/files/covid/COVID-19-CARES-Act-Funding-and-Expense-Reimbursement-FAQ.pdf

Is all this CARES Act money from the feds going to supplement ADA funding flows or is it only to reimburse specific expenditures by specific schools? Posted May 28, 2020Currently there are two large funding streams from the CARES Act that will impact K-12 education in the state. (There are also several smaller funding streams.) The ESSER fund flows to school districts. A portion of the ESSER fund would supplement expected FSP funding in district budgets (roughly 5% of the ESSER formula total per LEA, which would be used to cover any requested private school equitable services, but if no/fewer requests are received, would be extra funding for any lawful purpose). The remainder will be used as a source of funds for the Foundation School Program ADA Hold Harmless, and so would not be supplemental funding.The CRF is a reimbursement program. These are supplemental funds to school districts, intended to cover extra COVID-19 expenses.

See Q & A #2 (page 12) on this TEA document:
CARES ACT – Coronavirus Relief Fund (CRF)
https://tea.texas.gov/sites/default/files/covid/COVID-19-CARES-Act-Funding-and-Expense-Reimbursement-FAQ.pdf

How much reimbursement can we anticipate receiving under CRF? Posted May 21, 2020LEAs will be eligible for up to 75% of additive expenses incurred as of close of business May 20, 2020, to be reimbursed subject to a cap per LEA described below, and subject to CRF funding availability as described below. Each LEA will be capped at a reimbursement amount equal to the greater of $50,000 or an amount equal to $250 per compensatory education (SCE) student in the LEA. This would allow for every LEA, regardless of size or SCE student count, to receive at least $50,000 assuming they incurred at least $67,000 in underlying reimbursable expenses. For LEAs with more than 200 SCE students, their reimbursement would be capped at an amount equal to $250 per SCE student.

*ESSER: The Elementary and Secondary School Emergency Relief  (formula funding for emergency relief)

Federal stimulus funding appropriated by Congress to help states and school districts deal with the effects of the coronavirus pandemic could find its way into the coffers of private schools and virtual education vendors.
The Texas Education Agency published new guidance on CARES Act funding for school districts on May 21, 2020. Confirming the state’s decision to abide by the direction from Secretary of Education Betsy DeVos to expand eligibility for equitable services, the agency explains in its FAQ document that school districts must use their stimulus funding to offer equitable services to all private nonprofit schools within the attendance zone. TEA adds that the district must provide the services, as chosen by the private school, to any of the private schools who opt to participate. Under this guidance, school districts would not be forced to send the stimulus money directly to the private school for its own discretionary use, but the districts would have to pay for services requested by the private school. 

Teach the Vote https://www.teachthevote.org/news/2020/05/20/texas-signals-it-may-send-federal-k-12-dollars-to-private-schools/