Limit for requirement to inform HMRC of pension contribution

I'm planning to make a cash contribution into a private pension plan from my previous employer (i.e. the contribution will be done from my bank account rather than directly via my payslip/salary). This site indicates that "You must write to HMRC to make a new claim for a pension contribution over £10,000" https://www.gov.uk/tax-on-your-private-pension/pension-tax-relief I want to avoid doing that extra paperwork if I can, and I have three questions: 1) Does the £10k limit apply to the amount that I pay from my bank account? Or the total amount that gets added into my pension pot, after the pension provider applies basic tax relief at the rate of 20%? 2) Can I claim the remaining tax relief for this cash contribution via self assessment (I'm a higher rate taxpayer). 3) I've made other pension contributions this tax year to my current employer's pension plan, directly from my salary. The appropriate tax relief has already been applied at the time the contribution was made. Do these contributions count towards the 10k limit? Thanks!

Hi Esteban,
Yes, If the money is coming from your bank account, then you will have already paid tax on it through your employment, so you will need to claim the tax relief from HMRC.
This can either be in writing on in a Self Assessment tax return.
No they do not count towards the £10000 limit, however, they will count towards the pension threshold, which is up to £40000 or your gross income in 22/23 or £60000 or your gross income in 23/34.
Thank you.