Chromes are the brightest flats out there. If you need brighter still, I would say try Pressurewound strings. GHS Pressurewounds and SIT Silencers are good examples.
The black label 40-100s are similar tension to XLs.
The Super Brights are definitely more flexible/lower tension in the same gauge.
If you go for Super Brights, I would go up to 45-105 to get a similar tension.
TGI Extreme - £54. I use this for rehearsal and it holds my Jazz bass very nicely.
https://www.absolutemusic.co.uk/tgi-extreme-series-electric-bass-guitar-gigbag.html?source=shopping&sku=tgi4836